There was a long thread about this on here a few weeks ago with some of the military guys from TSR talking about it. Having read their views, and also cross referenced with some other stuff I found on the internet, the summary of how I understand it is:
- whilst it is true that the UK military has faced significant cuts, they still possess cutting edge military technology, so whilst our forces are small relative to others they can pack a massive punch
- the Argentinian military is a long way behind in terms of technology, they haven't moved forwards that much since 1982 whereas we are a long way ahead of the technology we had then (politically, because Argentina used to be ruled by military juntas like Galtieri's in '82, when they moved to democracy, the government always kept military spending low out of fear that the army would retake control....hence Argentina does not have much of a military)
- cuts to the Navy mean that retaking the Falklands would be more difficult if they actually fell, but the Falklands are now better defended than in 1982 and taking them in the first place would be difficult
- there are four Eurofighter Typhoon jets defending the Falklands which have such superiority over the Argentinian jets that they would be able to take out their entire air force without the Argentinians getting within firing/tracking range of the Typhoons. An air force commander quoted in the paper said that an air battle in the Falklands would be a 'turkey shoot' for Typhoon pilots
- without the ability to establish air superiority any invading ground forces would be dangerously exposed, as the defending ground forces could just call in air strikes onto them at will
- the Navy could send a submarine that would have the range to strike Argentinian mainland with Tomahawk cruise missiles, so if the Argentinians really did want to go to war with us, we could start destroying their military bases in their own country, and they would have no capability to respond at the UK
- there is a TA style territorial defence force of Falkland Islanders, trained by the British military, so even if the Argentinians did somehow manage to briefly take the Falklands, they would face local resistance that was professionally trained
In summary, the prospects of Argentina actually launching a military campaign and retaking the Falklands are remote, and to do so could be catastrophic for Argentina, as any attempted invasion could result in shocking losses to Argentina within the first few days, including the destruction of their entire air force.
So the tactics Argentina wants to employ is to build a general Latin American consensus against Britain over a long period of time, to make things awkward for the Falklands and make Britain feel that it's not a case of Britain v Argentina but Britain v Latin America. Although it might seem a long way off at the moment, if there was a genuine Latin American alliance against Britain, and it came down to military action, where the Brazilians, Venezuelans were fighting us as well then that would make things much more difficult.
However there are a lot of political consequences with that and it is a big step for the rest of Latin America to actually declare war on a nation like Britain, it might have been more credible if Latin America was being dominated by right wing military dictators as in the past, but their governments are generally run these days by socialists and trade unionists, although they regard the Falklands as an imperial occupation by the Brits, these types tend to oppose military action wherever it goes on. So it would be hard for Argentina to actually get them to sign up to fight.