I haven't tried testing it on the test server but I can say that with the latest Firefox on Win8.1 the problem is still occurring on the standard server. It seems to log me out most of the time in a couple of hours. I've even noticed that shutting down Firefox and restarting will log me out. (Though I suppose it's possible that was just a coincidental match up with the time that seems to occur every few hours. It's definitely a bit annoying especially when I try and add a comment only to have to scroll back to the login menu to login and then find out where I wanted to add a comment again.
Okay, are you using some sort of password management utility like LastPass? Because we had a case where a user was using that - LastPass was logging him in, but without "Remember me". So after a while, naturally, the user was logged out. Also keep in mind that permanent logins depend on cookies, so if you or any browser extension is blocking them, you won't stay logged in for more than the regular timeout (~30m-1hr). The fact that you're getting immediately logged out if you close FF tells me that the either cookies aren't sticking, or "Remember me" wasn't checked.
Other than that, we strongly believe that the problem is fixed on the server side now.