RNZ reports the 14 men, including a former prime minister, were jailed last year for taking bribes to cross the floor.
In September, 11 of them were given additional jailtime for conspiracy over the former speaker of parliament's decision to pardon himself and his colleagues while he was acting president last year.
The 14 men had sought to have the convictions overturned by claiming parliamentary immunity.
They told the court that they were attending a session of Parliament when they were prosecuted and this is prohibited under the constitution.