Three judges at the Court Martial Appeal Court in London yesterday rejected an application by Sergeant Danny Nightingale, 39, from Crewe, Cheshire.
Last July the special forces soldier was sentenced to two years' military detention, suspended for 12 months, by a military court in Bulford, Wiltshire, after being convicted for the second time — his original conviction was quashed in March 2013 by appeal judges and a fresh trial ordered.
He was found guilty of having a 9mm Glock pistol and more than 300 rounds of ammunition in the bedroom of his shared Army house.
Dismissing his application for permission to appeal, Lord Chief Justice Lord Thomas ruled that there was nothing in the grounds he wished to argue that affected the safety of his conviction.
Rejecting Nightingale's renewed application for permission to appeal, Lord Thomas, sitting with Mr Justice Hickinbottom and Mr Justice Jeremy Baker, said there was a "considerable amount" of evidence which "supported" the conviction.
Lord Thomas said the appeal court could not see "in any way" how his proposed grounds of appeal — the principal one related to expert evidence — would "affect the conviction".