Well, it depends. Usually, I believe it's connection specific. I'd guess 9 times out of 10 it's just something with your local internet connection. Of course, even then it depends on where these PCs are... are they at the same location (say, one in your bedroom and one in your living room) or at separate locations (one at home and one at work)? Say I have a PC connected here at home, and one connected at work. If my router here resets or otherwise loses its connection, then the AIM instance here will disconnect but the work one should stay consistently connected.
But, occasionally AIM does have trouble on the AOL side of things. In that event, there's usually a deluge of users all complaining "why can't i connect?" at the same time.