Attorneys in the case argued for about an hour before a three-judge panel at the 11th Circuit Court of Appeals, wrangling over whether Davis' lawyers had used the proper protocol in exhausting his options for a new hearing and whether evidence uncovered after his conviction warranted a fresh look at the case.
"Every time we got a piece of evidence, we brought it to the state's attention," said Thomas Dunn, one of Davis' attorneys. "I wasn't failing to present compelling evidence to the court."
State prosecutors maintain that the correct man was punished in the 1989 murder of Savannah Police Officer Mark MacPhail and that any claims to the contrary should have been made long before now.
"If this was such a compelling case of innocence ... they should've gone right to the trial court with the evidence," said Susan Boleyn. "You can't keep getting different bites at the apple."
The judges appeared especially interested in the circumstances under which someone who might be wrongly convicted could appeal that sentence.
"One of the problems in this case ... is that as bad as it is that somebody innocent could be executed ... it's also very possible that the real person who shot Officer MacPhail is not being prosecuted," said Circuit Judge Rosemary Barkett.
The MacPhail and Davis families sat across from each other at the front of the courtroom, which was also filled with media and supporters for both sides.
Davis' lawyers told the panel that they could only press the claim of their client's innocence after they had attempted a range of other appeals.
The hearing is the latest flashpoint in a case that has attracted widespread attention, sparked dozens of international protests and won Davis the support of former President Jimmy Carter and leading law-and-order advocates who say Davis deserves another day in court.
"Davis is not asking the court to set him free," former FBI Director William S. Sessions wrote in a recent column in The Atlanta Journal-Constitution. "He is asking for the court's permission to give his innocence claims the full hearing they deserve. Our justice system should punish the guilty, free the innocent and have the wisdom to know the difference."
MacPhail was working off duty as a security guard at a bus station when he rushed to help a homeless man who had been pistol-whipped in a nearby parking lot. The 27-year-old officer was shot twice when he approached Davis and two other men.
Witnesses identified Davis as the shooter in the 1991 trial, and prosecutors said he wore a "smirk" as he fired the gun. But Davis' lawyers have since argued that people who did not testify at the trial have said another man confessed to the killing. That man testified against Davis.
Prosecutors have long argued the case is closed. Savannah District Attorney Spencer Lawton also said he doubts the new testimony meets the legal standards for a new trial, and said the witness' changed statements invite "a suggestion of manipulation, making it very difficult to believe."
Davis' life has been spared three times in the past year, most recently, three days before his scheduled execution date, after his attorneys convinced the 11th Circuit Court of Appeals in Atlanta to stay the execution. Tuesday's hearing gave them one more chance to press their appeal.
As the case approaches the latest legal hurdle, the Davis and MacPhail families are in limbo. Davis' sister, Martina Correia, spoke after the hearing as the MacPhail family filed silently out of the courthouse behind the press conference and did not comment on the hearing.
"This is not family against family," said Correia. "We're fighting for justice for Officer MacPhail, too. But killing Troy does not get justice for him."
It is unclear when the panel will issue a decision in the case.