Safari reloads excessively, with unusual effects

Question

Starting today, Safari has refused to let me log into different websites. For some, right at the point that it appears to log in successfully, it suddenly reloads and goes back to the log in screen. For others, where I have previously clicked "keep me logged in" or an equivalent checkbox, it tries for a few minutes, and then comes up with
Safari can't display this webpage
Safari has repeatedly encountered an error while trying to display
"https://www.facebook.com".
It also affects some websites I don't have to log into.
I have closed safari and re-opened it. The problem is still there. I've reset safari. That didn't help. I followed the instructions in this article, but safari was still acting up, so I put everything back. I guessed that the problem was either safari or my computer either overheating (a frequent problem it has, which has been slowly getting worse as it ages) or failing to connect to the network. It was easiest to try another browser, so I did that first. Lo and behold, Chrome works, so I know the trouble is with Safari, not with my computer or its internet connection. I'm just running out of ideas of how to fix it.
The weird thing is, a few pages constantly reload until they come up with an error message, some only reload when I try to log in, and some are perfectly fine. I could view www.xkcd.com with no problems, but what-if.xkcd.com refused to load. Gmail only reloads (which causes logging out, as though the browser had been restarted rather than the page refreshed) right when the progress bar loading the inbox reaches 100%, before the actual messages appear. Pokefarm reloaded with the effect of causing me to be logged out every couple of pages that would load, until I checked the "automatically log me in" box one time when I logged back in, and now it only reloads the page every once in a while. Facebook (which I've left logged in near-permanently on my computer) refuses to load. My student account logs in, sometimes long enough to click the email link, then almost immediately goes to the "session has expired" link on both tabs. I'm not finding any particular pattern except that each website is consistent in how it acts. I'm really getting frustrated
Ideas, anyone?

Answer 1

Bee: Those are all good questions.
As a college student with a campus-wide network, I have no clue if anything's been changed, though we usually get emails about planned outages for maintainence. I also wouldn't know who to call. But as I said, my other browsers worked just fine (I specifically tried Chrome) so I'm pretty sure the trouble wasn't in the network.
The account with my name is an administrator, and I keep a second accont around, called "Admin" for when programs die and are harder to troubleshoot, mainly to figure out if I've just done something stupid and messed up my account rather than the whole program acting up. I didn't use that, because I tried another browser first. If that hadn't worked, I would have rebooted and seen if that helped. If that didn't help, then I would have experimented with the Admin account. I probably would have suspected the network at that point, and borrowed a friend's computer to test it.
Anyway, those two are the only accounts currently on the computer, and both are password protected. No one else has access to it, (even my roommate won't brave the disaster area that is my desk) and I didn't change any settings recently. I don't think I've downloaded anything in the past week or more. The last thing I installed was months ago. (That's the long version of "no new security apps")
That aside, I'm still not sure exactly what the problem was, but I think it was exacerbated by my laptop's heat issues. Because in the morning, Safari worked normally again. At that point, my computer had been asleep all night and had cooled down. If it had been off I would probably conclude that clearing the RAM helped, because it feels like memory is more closely related to how applications behave than heat is, but it was asleep and held onto all of my session data.
The issue is resolved as of ~16 hours after the fact. Is there a way to mark it as such?
I mean, I wouldn't mind continued discussion, in case that happens again, but it hasn't happened since. My computer has reacted much more predictably to heat and simply crashed. I think I like that better: I know what the problem is and how to fix it.