Lawyers representing Danny Nightingale tried to quash the conviction at another Court of Appeal hearing.
They told three appeal judges that Sgt Nightingale had been placed under "undue pressure" to plead guilty by a barrister who represented him at the military court hearing.
Lawyers argued that the conviction was therefore "unsafe" and Sgt Nightingale's guilty plea a "nullity".
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Trains on the route will be brought back under public control from Sunday, with the London North Eastern Railway brand being resurrected.
Drones and fireworks ensured the spectacle got off to a memorable start in front of 20,000 people.