Besides the fact that the persistence of any Argentine claim to the Falkland Islands is only slightly less defensible or precedent-based than the (*former*) Indonesian claim to Timor Leste (East Timor)...
...I'll defend that in detail, if you'd like. Remember, I'm as revanchist as they come *when there is an actual historical claim to territory*, I'll gladly go chapter-and-verse on why this "claim" is Nationalist claptrap and has been since Argentina managed by some grace of heaven to liberate itself from the Spanish Empire...
...anyway besides that, the fact is they tried aggression and ended up with all the moral justification for their position that Saddam Hussein had when his army was sitting in Kuwait. And then they got what was coming to them, even without an Article 5 NATO intervention or a UNSC authorization of force. Just little 'ol tired Britain (and a tiny handful of help) gave them just what they deserved and frankly they got off lightly with the only reprisal outside the campaign on the islands was the sinking of the General Belgrano... Yes, that's heartless of me to say so. Doesn't change the fact that had the Argentines pulled a stunt like that on a U.S. possession they would have been picking up the pieces of every airplane, rowboat and army barracks from Buenos Aires to Tierra del Fuego. Don't ask what Ivan would have done to them had it been their collection of turf and sheep.
But these days, Argentina (again, the Nation-State, not necessarily the ordinary citizen) seems intent on playing again... at least politically. With a steady growth in GDP for the islands and the recent petroleum exploration success, Falklands is on its way to returning the favor to the homeland for all the lives and all the years defending the place. Argentina, on the other hand, remains mired in one of the longest and ugliest economic collapses of the last century, vastly worse and longer lived than the current unpleasantness in the U.S.A. and Europe. The current Argie management, the regime of Cristina Fernandez de Kirchner (Yes, she married her way into politics. It's a local tradition after all.) is part patron and part client of Hugo Chavez' schemes of anti-just-about-anyone-halfway-decent
The U.K. side of things has been steady and measured (and more than Cristina and her political henchlings deserve, frankly). With the construction and constant operation of RAF Mount Pleasant, and a fairly good plan for rapid re-enforcement, there is also the stick available in case calm words and a few carrots don't keep the peace. None the less, it pays to be prepared.
In the words of Sara Jones (widow of Lt Col Herbert 'H' Jones VC OBE, 2PARA ):
"We stood up for what we believed in. We didn’t like to see a small country overrun by somebody who had very little claim to it."***
She told The Daily Telegraph: "The islanders have always been fiercely British and want to stay that way. I would like to believe that we would, if we could, do it again."
If you've not heard of 'H' before, this is of marginal value in telling about the man.
caveat: this and the Wikipedia links above are only for general reference. Please check all actual citations.