You're right, the major war prior to the Falklands was Vietnam, and the British didn't help out in that one, so I guess there was no reason the US felt obliged to help out a decade later in the Falklands.

I guess it really depends on US-Argentina relations, and also whether the UK looks like they actually need any help.

The US could at least help out covertly. "Whoops, the entire Argentinian Navy just exploded at once! I guess the British must have more submarines down there than we thought!"

Realistically from what I've read, Argentina is so militarily depleted nowadays, and the UK has learned so much from the previous war, that Argentina couldn't even win a war against the British forces garrisoned in the Falklands, let alone the reinforcements. There is no chance of a serious war... although when I went to Argentina last year I found there's still freaking road signs by the side of the road with a map of the Falklands and proclaiming "Las Malvinas son Argentinas" (or whatever the correct Spanish is)