AUSTIN, Texas — A second attempt by Texas lawmakers to bring a man on death row to the state Capitol over doubts that he killed his 2-year-old daughter failed again Friday, dimming the likelihood of Robert Roberson testifying publicly after a last-minute subpoena halted his execution. Roberson, who had been scheduled to be die by lethal injection in October, would be the first person in the U.S. to be executed over a conviction tied to shaken baby syndrome, a diagnosis that medical experts have questioned. The latest unsuccessful effort to have Roberson testify comes after Texas’ attorney general asked a court to block a second legislative subpoena issued by lawmakers, who are running out of time until the Legislature reconvenes in January and the subpoena expires. “We have been attempting to fight accommodation since October, and they have never responded to anything meaningfully because they don’t want to have Robert here,” said Democratic state Rep. Joe Moody, one of the lawmakers who led the effort to halt Roberson’s execution. Roberson, 58, was convicted of killing his daughter in 2003. Prosecutors argued that he violently shook his daughter back and forth, causing severe head trauma in what’s called shaken baby syndrome. A bipartisan group of lawmakers, civil rights advocates and medical experts have expressed doubts over the shaken baby diagnosis used to convict Roberson and say his daughter likely died from symptoms of severe pneumonia. The state’s Republican attorney general, Ken Paxton, has staunchly defended Roberson’s conviction and said the science around shaken baby syndrome has not changed enough to absolve his guilt. In the court order, Paxton’s office said that “it is not the role of the Legislature to adjudicate offenses” and that lawmakers overstepped their power when they halted his execution. The Texas House Committee on Criminal Jurisprudence issued their first subpoena for Roberson to testify one day before his scheduled execution — an unprecedent legal maneuver that successfully staved off his execution. A new execution date has not been set. Texas has a “junk science law” that allows people wrongfully convicted on dubious science to have their sentences overturned. The House committee said they wanted Roberson to testify about this law and how they believe it has not worked as intended for his case. Criminal justice advocates say the state’s highest criminal court has deliberately misinterpreted the law. The Texas Supreme Court ruled in November that although the subpoena was valid, it cannot be used to circumvent a scheduled execution. Republican Gov. Greg Abbott has maintained that Roberson was rightfully convicted. The Texas Board of Pardons and Parole voted unanimously to not recommend him clemency in October.