The seven escaped from the Connally Unit prison, about 60 miles southeast of San Antonio, in December 2000 and two weeks later were involved in a sporting goods store robbery in which a police officer was killed on Christmas Eve.
Halprin, then 23, was the youngest member of the gang and is one of four still on death row. He does not yet have an execution date set.
Halprin's attorneys had raised 31 claims challenging the validity of his 2003 conviction and death sentence from Dallas County. Among them were arguments his trial lawyers were deficient.
But the state's highest criminal appeals court, with no dissents, said the trial court in Dallas held five evidentiary hearings in his case and recommended his appeals be rejected. The appeals court agreed with the lower court's findings.
Halprin, now 35, could continue his appeals in the federal courts although court records show none have been filed yet. Gary Udashen, listed on state court documents as Halprin's appeals attorney, did not immediately respond to a call Wednesday from The Associated Press.
Halprin was convicted in the death of Aubrey Hawkins, a 29-year-old police officer in the Dallas suburb of Irving, who was gunned down when he interrupted the gang's sporting goods store robbery.
Rewards for information leading to the gang's capture reached $500,000. A tip led authorities in January 2001 to a trailer park outside Colorado Springs, Colo., where Halprin and three partners were caught. A fifth gang member, Larry Harper, committed suicide as police closed in. The two remaining fugitives were caught two days later about 20 miles away.
Two of the gang members have been executed, one in 2008 and one last year.
Along with Halprin, those still on death row are Patrick Murphy Jr. 51; Joseph Garcia, 41; and Donald Newbury, 50. Newbury was set for injection a year ago when he received a reprieve from the U.S. Supreme Court.
Halprin was serving a 30-year-sentence from Tarrant County for injury to a child when he escaped.
He contended at his trial that he didn't participate in shooting Hawkins. In a prison interview with the AP in 2003, he called the officer's slaying "beyond stupid."
In other rulings Wednesday, the court rejected appeals from two inmates on death row for Harris County slayings.
William Michael Mason, 59, was condemned for the abduction and beating death of his wife in 1991. Ray McArthur Freeney, 39, received the death penalty for killing two prostitutes in 2002. Neither has an execution date.
Take ABC13 with you!
Download our free apps for iPhone, iPad, Android and Blackberry devices