Hval,
The Argentine government seems to be in that spiral as you described but they would soon lose what ever international support they have if they took offensive action. The UK could repel most forms of military attack however any 'show of force' by Britain - over and above what we've deployed would be read as overt aggression - which no one wants. Following the address given by their FORMIN last night, any 'aggressive' act by the UK would simply fit his narrative of the UK militarising the region. It's a matter of getting the balance right.
The UK has made it quite clear that the FI are non-negotiable; an internationally astute move would be for a referendum to be held amongst the locals. Although the outcome would be resoundingly supporting status quo ante, the domestic political damage to Cameron would be enormous. He would be accused of weakness, of caving in etc and it could prove fatal to the coalition government. Now there's an opportunity!
Seriously, I think the UK has pitched this about right. Proone - The FI are an anachronism, as are the Channel Islands and Gibraltar - but hey are British and want to remain so, so the Government is obliged to defend them.