I have had the problem of being repeatedly and rapidly logged off, on both FiberglassRV and EscapeForum as other have mentioned. It has happened occasionally for a brief period (an hour or a day) scattered over a period of many months, so it is presumably unrelated to the most recent "upgrade". It is extraordinarily frustrating, as I can log in, see the successful login dialog, and be logged out on the first load of the forum page. Even if I get a logged-in forum page, I can post a response because I get logged out (as if my session had timed out, but far too soon) before I can submit my post. When this happens, I just give up.
Clearing the brower cache is ineffective, which makes sense because this is a server issue, not a browser issue. Disconnecting my (mobile) internet connection and reconnecting seems to occasionally help, suggesting that the server is having difficulty with session management.
I do not want to stay logged in indefinitely; I don't mind logging in once per session, and this faulty behaviour is not related to the "stay logged in" option. The "remember me" option has not worked for me on any machine with either forum, ever, and I just don't worry about that, as the browser remembers login credentials even though the server fails to (or fails to use a cookie with this information properly). This behaviour will depend on cookie handling; I do permit the forum site to place cookies on my machine.
I don't know if this is brower-dependent, as I essentially don't bother with any brower other than Chrome now.