I just tried logging out and back in on both Chrome and Firefox on a Windows machine with no issue. I've also used it on my iPad and my phone, no login issues.

I'll see what one of the admins has to say, but if I had to guess, I'd say it sounds like a browser/cookie problem. Do you have an overzealous plugin trying to delete cookies or something?

I know this is just a workaround and not a solution, but do you really have to log out? Are you sharing the computer and you don't want someone else seeing your login info?