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".
More top news
Hundreds of passengers escaped down emergency slides as smoke on a Korean Air Lines plane forced a mass evacuation before take-off.
The Prime Minister has insisted that Britain support the new Libyan government and help to stabilise the region.
Why did David Cameron decide to remain silent on a subject seen as vital to many voters in the referendum campaign? I asked him, to find out