By Dakin Andone, Ed Lavandera and Cindy Von Quednow, CNN

(CNN) — Death row inmate Robert Roberson did not appear Monday to testify before the Texas House Committee on Criminal Jurisprudence – in person or otherwise – despite a subpoena lawmakers issued last week that halted his execution for a crime he and his attorneys say did not occur.

After a weekend of uncertainty, committee Chair Rep. Joe Moody said he did not believe Roberson would testify at Monday’s hearing, which will feature the inmate’s case and the shaken baby syndrome diagnosis his murder conviction was built upon.

While the Texas attorney general’s office has sought to limit Roberson to testifying virtually, Moody did not feel that would be appropriate given Roberson’s autism, he said. The committee and Roberson’s attorneys had expected he would appear in person at the Capitol in Austin.

This does not mean Roberson will not eventually testify, Moody added, saying the committee remains in talks with the attorney general’s office.

“I expect a quick resolution to these discussions, which are ongoing, even at this moment,” Moody said.

Roberson was scheduled to be executed last Thursday for the 2002 killing of his 2-year-old daughter Nikki Curtis – who allegedly died from shaken baby syndrome. But the execution was halted after the Committee on Criminal Jurisprudence issued a subpoena for Roberson to testify about his case, an unprecedented gambit that led to a partial stay of execution from the Texas Supreme Court.

Lawmakers intended to hear from Roberson in person as they considered the lawfulness of his case, and whether it necessitates changes to a “junk science” law those in his corner feel should benefit Roberson. Over the weekend, however, members of the committee, the inmate’s attorneys and the office of Texas Attorney General Ken Paxton clashed over the logistics of his testimony.

In the meantime, the committee was proceeding with the hearing, which included testimony from a slate of other witnesses, including TV host Dr. Phil McGraw, who has interviewed Roberson, and the author and Innocence Project board member John Grisham.

Committee members had continued to signal Monday morning they expected the inmate to appear before them in the flesh.

“I fully expect him to testify today, and if not, we’re going to make reasonable accommodations to ensure that his testimony is heard before this committee sooner rather than later,” Rep. Jeff Leach, a Republican, told CNN’s Erica Hill.

“The question now is whether he’ll show up today, whether he’ll show up at another date here at the Texas Capitol, or, if necessary, whether our committee will take a field trip … to interview him in a public hearing there at the prison.”

At the same time, the attorney general and the committee were filing dueling motions with the Texas Supreme Court over its decision to temporarily halt the execution. GOP Gov. Greg Abbott submitted a letter brief in support of the attorney general’s filings, arguing the committee’s subpoena had violated the state constitution’s separation-of-powers clause, effectively usurping clemency power that is reserved for his office.

The brief notes Roberson was convicted more than two decades ago, and that if the Legislature wanted to seek his testimony, it had ample time do so. “Only at the eleventh hour, when the Constitution empowers the Governor to make the last move, did the House Committee decide to violate the Separation-of-Powers Clause,” the brief says.

In an order Sunday, the court said it was still considering arguments from both sides and set several deadlines for filing over the next several weeks.

Texas law requires a judge to set a new execution date at least 90 days in the future, and Roberson’s attorney previously told CNN the earliest a new execution could be set would be next year.

The testimony

McGraw interviewed Roberson earlier this month on TV and indicated he has extensively gone over the trial transcript and medical record involved in the case.

He testified the case against Roberson was tried as a shaken baby case and the term was brought up 47 times during the 2003 trial, despite evidence Roberson’s daughter was very ill at the time of her death.

“I am 100% convinced that we’re facing a miscarriage of justice here,” McGraw testified. “I think if people really drill down on the facts of this case and thought … you can be executed against a standard of reasonable doubt, I think it would be horrifying. I don’t think he’s had due process, I don’t think he’s had a fair trial, and I think he should.”

Grisham, a bestselling author who wrote an op-ed on Roberson’s case, commended the committee’s actions last week, saying members “literally saved an innocent man’s life.”

“You took a bold stance against injustice at the precise moment when the courts and the leaders of the state seemed hell bent on executing Robert. If not for you, Robert would be in his grave today. Your actions were creative to say the least, fascinating, unique, courageous, bipartisan and heroic.”

During his testimony, Grisham advocated for a retrial.

“Let’s have a fair trial, that’s all we’re asking for,” he said.

Terre Compton, one of 12 jurors in Roberson’s trial, said the jury’s decision was based on what was presented to them about shaken baby syndrome, and nothing else.

She testified if other evidence or explanations had been presented, she would have found Roberson not guilty, and she now believes he did not kill his daughter.

“I could not live with myself thinking that I had a hand in putting an innocent man to death,” Compton said.

In an interview with CNN after her testimony, Compton said learning about Roberson’s potential innocence has weighed on her so much that it would move her to tears.

“I don’t think it really hit me so hard until they set his death date,” Compton said. “We as jurors took what they told us to be the truth. … I feel like we were taken very much advantage of. I think they lied to us in a lot of ways.”

The case

For Roberson, the committee’s subpoena last week was a godsend, coming just as the other doors to save his life slammed shut: His team had lost several appeals in the Texas courts, the state Board of Pardons and Paroles had declined to recommend clemency and the US Supreme Court had also declined to intervene.

Roberson was convicted of capital murder in a case that relied on allegations his daughter died of shaken baby syndrome – a misdiagnosis, his attorneys claim, and one they say has since been discredited. Child abuse pediatricians and medical organizations such as the American Academy of Pediatrics remain firm on the legitimacy of the diagnosis.

But Roberson, his attorneys and advocates point to a variety of other possible causes for Nikki’s death, citing their own medical experts: She had double pneumonia that had progressed to sepsis, they say, and she had been prescribed two medications now seen as inappropriate for children that would have further hindered her ability to breathe. Additionally, the night before Roberson brought her to a Palestine, Texas, emergency room, she had fallen off a bed, and was particularly vulnerable given her illness, Roberson’s attorneys say. They point to all these factors as explanations for her condition.

Roberson brought Nikki to the hospital on the morning of January 31, 2002. He told investigators he had woken in the night to find she’d fallen off the bed, with some blood on her lips and a bruise under her chin, according to the criminal complaint. He kept her up for two hours to make sure she was OK, he said, but when he woke that morning, she was unresponsive.

Doctors treating Nikki presumed abuse based on her symptoms and common thinking at the time of her death without exploring her recent medical history, the inmate’s attorneys claim. And they say his behavior in the emergency room – viewed as uncaring by doctors, nurses and the police, who believed it a sign of his guilt – was a manifestation of autism spectrum disorder, which went undiagnosed until 2018.

Indeed, police never explored explanations for Nikki’s death other than shaken baby syndrome, according to Brian Wharton, the former lead detective of the Palestine police. The guidance of medical experts paired with Roberson’s demeanor led authorities to focus on Roberson as a suspect “to the exclusion of any other possibilities,” he has told CNN.

The diagnosis

Roberson’s attorneys do not dispute babies can and do die from being shaken. But they contend more benign explanations, including illness, can mimic the symptoms of shaken baby syndrome, and those alternative explanations should be ruled out before a medical expert testifies with certainty the cause of death was abuse.

Shaken baby syndrome is accepted as a valid diagnosis by the American Academy of Pediatrics and supported by child abuse pediatricians who spoke with CNN. Today, it is more commonly referred to as a type of “abusive head trauma,” a broader term doctors began to use around 2009 to reflect it can be caused by actions other than shaking, like an impact to a child’s head.

Abusive head trauma generally occurs when a frustrated parent or caregiver violently shakes a child and/or causes a blunt impact injury, the US Centers for Disease Control and Prevention and others say. It is the leading cause of child abuse deaths in children younger than 5, the CDC says.

Criminal defense lawyers also have oversimplified how doctors diagnose abusive head trauma, child abuse pediatricians say, noting many factors are considered to determine it.

Still, courts across the country have been reconsidering the role shaken baby syndrome plays in convictions that rely upon it: Since 1992, courts in at least 17 states and the US Army have exonerated 32 people convicted in shaken baby syndrome cases, according to the National Registry of Exonerations.

Those who question the diagnosis point to research they say undermines its reliability. But within the context of the law, they are also concerned the diagnosis appears to encompass multiple elements of a crime, including the suspect, their state of mind and how the crime was committed.

“It’s the entire case, and that is Mr. Roberson’s case,” Keith Findley, professor emeritus with the University of Wisconsin Law School, testified before the Texas Committee on Criminal Jurisprudence last week. “When you have a prosecution, a conviction that rests entirely upon medical, scientific opinion, and it turns out that medical science is, at best, deeply disputed, you have a recipe for real problems.”

Child abuse pediatricians, however, fiercely defend the diagnosis.

“I don’t know what to say about the legal controversy,” Dr. Antoinette Laskey, chair of the American Academy of Pediatrics’ Council on Child Abuse and Neglect, told CNN. “This is real, it affects children, it affects families.”

The 2013 law

Last Wednesday, the criminal jurisprudence committee held another hearing about Roberson’s case, and whether he should have benefited from a Texas law commonly referred to as the “junk science writ.” The law, formally known as Article 11.073, dates to 2013 and was meant to open a path for someone to challenge their conviction if there is new scientific evidence that was unavailable at the time of their trial.

Roberson’s advocates feel he should have benefited from this law. The Texas Court of Criminal Appeals issued a stay of execution in Roberson’s case in 2016, sending a claim under Article 11.073 (among others) back to the trial court. The lower court ultimately ruled against Roberson, finding he had not shown there was new scientific evidence relevant to his case, and the appeals court later accepted these findings.

“I believe that section 11.073 simply did not work as it should have in the Robert Roberson case,” Findley testified last Wednesday – a sentiment echoed by members of the House committee, who signaled last week’s hearing was as much about Roberson as it was about finding a way to fix a law they felt had failed to operate as intended.

“Every member of this committee has been surprised by how it has been applied in this particular case,” Moody, the committee chair, said of Article 11.073. “Quite frankly, we’ve reviewed this case in detail, fully expected that this law would provide relief, and that has not happened.”

“When the Legislature passes a law and finds out that it’s not working the way that it was intended to, it is incumbent upon us to step in and make that law right.”

CNN’s Ashley Killough and Nicole Chavez contributed to this report.