Update on the situation:
I've tried some other things, and the problem persists whether or not my antivirus is running. The problem also crops up much more often at night, which would perhaps suggest a traffic problem with AIM, but if it's kicking me off that often because it can't handle its own traffic it and I have a problem. I've also had problems with webpages not loading on the first try, but when I refresh the page it loads fine.
Personally, I suspect the router may get overheated by nighttime and start dropping certain connections. I only notice when it drops AIM because the dropout is so brief that I'm usually not loading a new webpage or performing other internet tasks at exactly the same moment it occurs, but sometimes I do catch it, hence webpages sometimes loading and sometimes not. AIM notifies me when it goes offline, so it's more noticeable there. Any technical people want to tell me if this makes sense?
(edited for typos--I really shouldn't post things at night)
Edited by CopperPennies, 30 May 2010 - 10:24 PM.