I’m using Firefox 37.0.2 and I experience the same problem.
1) It never happens spontaneously, only when I click something.
2) It doesn’t seem to matter what I do. Clicking anything to navigate to a new forum or read a post, I suddenly get the guest user interface. (Login or sign-up...)
3) When that happens, if I click the browser back button, I get back to the previous page and I’m still logged in. I can read alerts, etc as usual but navigating to any other page returns me to the guest user interface.
4) When I suddenly find myself logged out, I find that my username continues to appear in the list of logged-in users. If I click on it it says “XXX was last seen 3 minutes ago....”