Aiden Hulme, who is alleged to have planned a Real IRA bombing campaign in England, failed to overturn his conviction on Thursday.
Hulme was sentenced to 20 years after being found guilty of conspiring to cause three explosions in 2001, including one outside the BBC Television Centre, west London.
Mr Justice Gibbs, who sentenced Hulme two years ago, said it was a “mercy” no one had been killed by the devices, which had been designed as “threats to the country as a whole”.
Defence QC Richard Ferguson told the Appeal Court that the trial judge had been wrong to allow anonymous text message evidence to go before the jury.
The first, declaring “up the Provos, up the Provos” was presented by the Crown as a “congratulatory expression” following a succesful operation, but was described as ambiguous by Ferguson.
Another message containing the words “fizzing sticks” and the question “what were you at last night” was also challenged.
The identity of the sender had never been established, but the prosecution was allowed to argue that the messages were part of “a conspiracy”. This was described as an “incredible” leap of logic by Feguson.
However, Orlando Pownall QC, for the crown, told the court there was “clearly” prima facie evidence allowing a jury to conclude the texts had come from a conspirator.
The jury would have been entitled to ask itself “whether a terrorist cell already operating in this country would have need to contact others out of the jurisdiction”.
“It is in circumstances that a terrorist cell operating on the mainland requiring support, influence, encouragement and help from conspirators operating in Ireland, that the text messages have to be viewed,” Mr Pownall added.
After a short retirement, Lord Justice Kennedy, sitting with Mr Justice Treacey and Mr Justice Wilkie, refused the appeal.
“We have carefully considered the submissions made to us by Mr Ferguson and Mr Pownall and have come to the conclusion that this appeal against conviction must be dismissed for reasons which we will give in writing in due course.”
The panel also refuse an application for leave to appeal against sentence by a Noel Maguire, who is serving 22 years for the RIRA attacks. Both men are serving their sentences at Belmarsh prison in south-east London.