last 50 years, the British military capability has advanced 50-60 years, whilst the argies are still using a lot of 1980s kit. I believe their amphibious craft which would be vital to the success of any invasion are now rotting somewhere and not exactly ready for action.
If they could get past the destroyer parked in the way (usually an air defence destroyer) they'd have to take out the airbase as a matter of urgency. Whilst the Argentine special forces are quite well respected and could probably mock up a civilian plane in trouble, leap out and shoot lots of things, this still wouldn't guarantee success given the sheer numbers of infantry we have there.
Whilst we only have a couple of jets stationed there, they'd be easily re-enforced by air as would the infantry.
The tactical situation at the moment is such that if they did try to invade they'd get a serious, serious pounding and would have to succeed in achieving air dominance, something which can not be done with both the air base and the air defence destroyer in position. Even if they managed to disable / destroy those (the defences of which are way in advance of anything they have), we would re-enforce quickly using paratroops with the navy being on its way.
Our huge deficit is that we currently use a slow, crap, part time French aircraft carrier which I'm sure they would not allow us to use for the purposes of waging war. This, though is not the biggest issue as we have significant overflight privileges over many countries and with mid air refueling / long range fuel tanks, it wouldn't be a huge issue to get more planes there - as long as the airbase is intact.
Plus they can't afford it.
EDIT: We can't afford it either.