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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The hunt for murder suspect Jed Allen has ended after police found his body two days after discovering his mother, stepdad and sister dead.
A woman who had been searching for her mother for more than 10 years has been reunited with her after posting an appeal on social media.
Although a dull start can be expected, it will brighten up in eastern areas. Especially to the south.