Please understand that there is just not going to be a repeat of 1982. The situation, military and political, is completely different.
Differences:
- Although the RN has been drastically run down in terms of fleet numbers, man power and funding since the 1980s, it is still completely modernized. The Argentinean military has been neglected even more the British (what does this tell you about Argentinean intentions about trying to take the islands by force?), and is still at 1980s levels. In 1982, only two RN ships had modern anti-air defenses (one of which shot down 3 of 4 attacking skyhawks in about 20 seconds), for example, now they all do.
- The British have an air field there now with a 1000 man garrison and four eurofighters (against Argentina's ~35 50s and 60s era fighters). As long as that airfield remains, the islands can be re-enforced by air.
- The modern Royal Navy has plenty of amphibious units it didn't have in the 80s.
- A major cause of RN difficulties in the 80s was lack of airborne early warning - Argentinean pilots flew in low to avoid detection by ship radar before popping up to release exocets. We have air born early warning now.
- The US stayed out of the conflict in the 80s because it had the Soviet threat to worry about, and the Argentinean Junta was a key regional ally in preventing the spread of communism. In 2010, there's no Soviet threat to worry about and Britain is a key ally in Afghanistan and Iraq. Expect more overt US support.
- The 'attack on one is an attack on all' clause of NATO isn't geographically limited any more. There may be NATO help as well.
- Argentina is a democracy, and has ruled out using force to try and reclaim the islands.
- Even when Argentina was ruled by a brutal Junta it only attacked because it thought Britain would not bother to respond: there can be no illusions on this point now. One such signal which lead Argentina to believe no respond would be made was the withdraw of the warship kept in the area. Today, there's a patrol boat and a RFA tanker (filling in for HMS Endurance, which is broken) and a Type 42 destroyer on the way south. It's exactly the opposite situation.
- Even without all the above, one SSN lurking in the area could stop an invasion dead in its tracks.
So, no. There will be no second Falklands War which will bankrupt GB and Argentina. Assuming (big assumption) that this every amounts to more than sabre rattling by the Argentinean government for the benefit of their voters (also remember that the claim to the Falklands is written into their constitution and a leader who doesn't persue the claim could be charged for violating their constitution, so they have to at least be seen to be making an effort), the most you will ever see on the war front is maybe a few ships firing across each others bows or something.

