The prominent Republican of Ballybinaby, Hackballscross, County Louth is almost one year into an 18-month sentence.
Just a week before Christmas 2015, Thomas Murphy was found guilty on nine counts of failing to make income tax returns between 1996 and 2004.
He was convicted following a 32-day trial before the non-jury Special Criminal Court and was jailed for 18-months last February.
The main thrust of his appeal was that he was denied a fair trial.
He claimed certain evidence shouldn't have been allowed and he accused the judges of failing to provide any adequate reasons for its decisions, including the ultimate verdict of guilt – thereby hampering any potential appeal.
In any event, his appeal has been unsuccessful.
President of the Court of Appeal Sean Ryan said it was difficult to summarise why but their reasons are set out in a 94-page judgement which was handed to his legal team this morning.
Mr. Murphy has now been given time to consider whether he wants to appeal the length of his sentence.
