UK has no hope to win this time if you people don't meddle. THey will be fighting against 3 major powers of South America this time, without an aircraft carrier, defense budget cuts and already fixated military in Afghanistan. While Argentines are weak themselves, with the more socialist new Brazilian government (very pro-Pan-South American) and a rather unrelenting Venezuela (building a powerful military force for the region), will make Royal Navy's life a living hell in the Falkland region. Simply because UK is not an expeditionary force anymore and is at its weakest.
They cannot even use the nuclear threat because that will cause a nuke rush in South America. That's the last thing you Americans want.