Zuma and the National Prosecuting Authority (NPA) had argued that the judges were wrong to find that then NPA head Mokotedi Mpshe had acted improperly when withdrawing the charges against him in 2008.
The court found that there was no reasonable prospects of another court reaching a different conclusion and that no compelling reasons for appeal were raised.
A full bench ruled last month that the 2009 decision to withdraw criminal charges against Zuma was irrational and set it aside.
Deputy Judge President Aubrey Ledwaba dismissed the application.
He says, "We seriously considered whether the appeal would have reasonable prospect for success and came to the conclusion that there are no merits in the arguments raised by the applicants. We have carefully reconsidered our judgment and conclude that the appeal does not have reasonable prospect of success.”
