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I had thought it was pretty much an issue that had gone away - I think looms larger in the cultural sensibilities of the Argentinians than over here in the UK though.
Going back to 1982, there was no formal declaration of war - rather the Argentinians sent out a force to "reclaim" territory they considered theirs - we sent a force to defend our sovereign territory.
I seem to recall that, prior to Galtieri actually invading, the ruling military junta was incredibly unpopular, so the invasion could be considered a means to boost popularity. Many analysts have commented that Mrs. Thatchers domestic popularity was pretty low, and that the UK military response certainly boosted her popularity and deflected attention away from some of the domestic political issues of the time.
So it could be considered as a war of politcal misdirection and expediency.
My thought is that the UK defence forces are at full stretch with NATO commitments in Libya and the ongoing conflict in Afghanistan - Add to that the defence budget cuts and lack of a Carrier and I think were the Argentinians to be opportunistic, the outcome of another "reclamation" effort by them might be rather different .
I suppose the threat is always going to be there until the Argentinians either give up their claim, or we cede our sovereignty.. And if oil is found in the area, that will certainly up the stakes...