I've been having this problem for a couple of days. I'd keep getting logged out, even when the browser (Firefox) was left open. Some times when I tried to re-login nothing would happen and I was redirected to the front page. Logging in through facebook would not work at all.
Just now I deleted all cookies relating to geocaching or facebook and updated firefox (I know it's bad testing procedure to try two fixes at once, but firefox updated itself automatically when I restarted).
Now at least I was able to log in through facebook, which is an improvement. Time will tell if I keep getting logged out. If so I'll report back.