The court's decision comes despite calls from Nobel Prize winners and international legal groups to review the case.
Ruben Campa, Rene Gonzalez, Gerardo Hernandez, Luis Medina and Antonio Guerrero had argued during their original trial that anti-Castro sentiment and high publicity surrounding the case in the Miami community would bias the jury against them.
Ahead of the hearing their defence lawyers sought to have the case moved to the town of Fort Lauderdale in Florida.
However the judge presiding over the case at the time ruled the defendants had failed to show it would be virtually impossible to get a fair trial in Miami, a decision later upheld by the appeals court.
The men are celebrated by many in Cuba who see them as national heroes who were spying on armed exile groups in Miami to prevent attacks on their country.
However, to anti-Castro members of the Cuban exile community in Miami, Havana's support for the men is seen as an example of an anti-US agenda in Cuba dating back to Castro's 1959 revolution.