The trio, including Richard Dart, a convert to radical Islam who has featured in TV documentaries, were sentenced to additional monitoring in the community after their jail terms.
They had argued during their appeal that the punishment was unfair.
But the Court of Appeal has ruled the sentences were justified because of the dangers the men posed.
It means a string of sentencing hearings for Syria-related terrorism offences, which had been on hold pending the ruling, can now go ahead.
The three men had all admitted preparing for acts of terrorism.
Each was given an extended sentence - meaning a jail term plus additional monitoring on licence in the community - last April.
Dart, from Weymouth, sought training in Pakistan and then discussed plans to attack Royal Wootton Bassett, the town that was the focal point for the repatriation of soldiers killed in Afghanistan, with others in the UK.
The other two men, Zahid Iqbal and Mohammed Sharfaraz Ahmed, from Luton, had prepared for a possible attack on Luton's Territorial Army base.
Dart received a six-year extended sentence, meaning he must serve at least two-thirds in jail before he can be considered for release on licence.
At the end of those six years, he will be subject to a further five years of monitoring under licence in the community.
He would face the risk of being sent back to jail if he committed another offence during that time.
Iqbal and Ahmed received extended sentences of just over 16 years - comprising an 11-year jail sentence plus an extra five on licence.
Rejecting their appeals at the Royal Courts of Justice, Lord Justice Pitchford said the judges who sentenced them had followed the appropriate procedures to assess each man as posing an ongoing danger to society.
Dart, who changed his name to Salahuddin al-Britani, became involved in extremism after moving from his home town in Dorset to east London.
His beliefs were brought into the spotlight in 2011 as part of a BBC television documentary My Brother The Islamist, by his stepbrother Robb Leech.
This was followed by a second documentary, My Brother the Terrorist, earlier this year.
Three men who challenged their extended sentences for preparing terrorism offences have lost their appeals.