Three judges at the Court Martial Appeal Court in London rejected the application by Sergeant Danny Nightingale, 39, against his conviction for illegally possessing a gun and ammunition.
Dismissing his application for permission to appeal, Lord Chief Justice Lord Thomas ruled that there was nothing in the grounds he wished to argue which affected the safety of Nightingale's conviction.
Last July the former SAS sniper 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.
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.
More top news
Overnight it will be cooler and fresher but most places will stay dry with a nippy start to Sunday.
X Factor contestant Raign seems to impress the Wembley audience with her own song even though Cheryl finds her "really annoying".
YouTube superstar Alfie Deyes got a sense of how far he has come when thousands of fans descended on his latest book signing in London.