The argument relied on a seldom-used legal principle known as 'ex turpi causa', which holds that a party cannot bring a claim if they have acted unlawfully.
They also argued their actions were protected because they were intended to protect others - an argument based on the claim that the intelligence processed at the Waihopai facility had been used by US and British forces to direct attacks in Afghanistan and Iraq.
But the Court of Appeal dismissed the appeal on both grounds, leaving it open for the Crown to seek damages.
In their judgment, Justices Tony Randerson, Lynton Stevens and Douglas White also ordered the men to pay costs in relation to the appeal hearing.
The court rejected the 'defence of another' argument, noting the appellants had no way of knowing whether an immediate risk to others existed, and had no way of knowing if their actions in damaging the radome would prevent that supposed peril.
The appellants were also unable to show their actions were proportionate to the damage they caused.
The court also rejected the 'ex turpi causa' argument, noting that case law strongly supported that the defence was not available in the circumstances of the case.
Speaking outside court in May, Mr Murnane said the men would not pay damages if the appeal was unsuccessful.
"We have no intention of paying a cent, even if I had it, because I don't believe it's a just case."