There will be no war.
The Falklands in 2013 are far more heavily and closely guarded by the British military than they were 31 years ago. In contrast Argentina is far weaker militarily than it was at the time. The technological gap between both countries has widened greatly since then.
Argentina's military has no power projection capabilities. They probably wouldn't win a war against Uruguay, whose population is less than 4 million. 30 years+ of technological advances have blessed Great Britain with satellite capabilities that would spot Argentine forces massing very much in advance. Argentina would not have the element of surprise it had in 1982.
Moreover, the Argentine economy is struggling yet again. Cristina Kirchner is a corrupt leftist and statist who is using state power as her predecessors did to plunder the nation's resources for her and her cronies' gain. You liberty lovers hate capital controls, eh? Well, Argentine banks now obligate Argentine citizens who travel abroad and use their credit cards in other nations to pay a percentage on all their transactions. And, the quantity of pesos they can exchange for USD is very limited. Yes, we who love sound money and follow Austrian economics know the USD is just a piece of paper, but in the Third World, the USD is still very much seen as a safe haven. Even in other nations in that area, like Brazil, whose economy is light-years ahead of Argentina's, wealthier Brazilians whose lifestyles are superior to the standards of living of many Americans often exchange their local currency holdings into USD. The Argentine people, barring the elite, are not doing all that well. Unemployment is high, and Kirchner and her government are widely disliked.
For her to launch an attempt to retake islands whose inhabitants are culturally, historically, and even racially British and who wish to remain an overseas British territory would be foolhardy, counterproductive, expensive, and it would earn her republiqueta of a country international scorn, even more than it did when her predecessors attacked. Outside of South America and perhaps Spain, the Argentine claim has no foreign support, and even if every country on Earth including the United States supported Argentina's sovereignty claim, Britain would never relinquish the islands, whether by negotiation or by force. The Brits are a proud people; they shed blood, spent money, and lost pilots, seamen, and ships while fighting Argentina in 1982. They would do it again - for pride, but also, because they firmly believe (and with very much just cause and historical claims) that the islands are legally and rightfully British.
Argentina will NEVER attack, and Argentina's flag will never fly over those small islands.
Nothing to see here. Move on now.