The 4-3 decision, issued early Monday, caps an appeal that has drawn national attention from anti-death-penalty groups such as Amnesty International, which argues that Mr. Davis' capital conviction in the 1989 slaying of off-duty Savannah police officer Mark MacPhail might execute an innocent man.
Seven of nine eyewitnesses who helped convict Mr. Davis in 1991 have since recanted their testimony. The high court's majority opinion said it took those arguments into account in issuing its ruling.
"Particularly in this death-penalty case, we have endeavored to look beyond bare legal principle ... to the core question of whether a jury presented with Davis' allegedly-new testimony would probably find him not guilty or give him a sentence other than death," Justice Harold Melton wrote for the majority.
The evidence, wrote Justice Melton, was not enough to grant Mr. Davis' appeal.
Prosecutors noted during last fall that most of the recanted witness statements offered by Mr. Davis' lawyers weren't taken under oath, as was the original testimony. They also argued that Mr. Davis' attorneys should have raised their concerns earlier in the appeal process.
Mr. Davis' family and supporters slammed the ruling.
"It is outrageous that four of seven justices are putting technicalities before my brother's life," said Martina Davis-Correia, Mr. Davis' sister.