I've been away but wanted to pop back and say that I'm still having this issue and am not sure why. I have cleared my site cookies, check 'Remember Me' every time, and have logged in to 3 different browsers (Firefox, Chrome, IE) and each time been logged out after no more than a minute. It doesn't even happen on the forum (or anywhere else), just on the main RPH site.
I have Sophos as antivirus and it isn't blocking the site, and Windows Firewall is turned off. Obviously it's a network problem of some kind - is there any more info I can provide to make more sense of it? I ran a normal, successful tracert & constant ping to rpheaven.org with no drops whatsoever.