I would just like to repeat, that i don't have any such problems. I log in, don't check 'keep me logged', and i'm happily logged in until i restart my browser, sometimes even after that.
I have 3 computers directly on the Net, none of them has such a problem. I will be installing a couple of Linux boxes, will try it there too.
WinXP SP2 patched to SP3, FF 3.6.10.
Again, i'm willing to answer questions about my config, if anyone is interested.