Quite recently I was facing a problem, where Firefox kept on forgetting my login information for sites once I restarted it, this was a bit annoying and given the lack of time I had, i never got around to debugging it.
I always chose websites to remember me forever, so getting having to login each and every time I restarted the browser started to become a pain.
However a article by Amit from Digital Inspiration was a eye opener to me, and I did find a solution to my problem in it.
My problem with Firefox logging me out everytime I restarted the browser was due to the fact that somehow the cookie settings were set to only be kept until I was using Firefox, they expired once I closed Firefox or restarted it.
Changing the value to they expire from the dropdown solved my problem of Firefox forgetting the login information every time I restarted it.
If this is not your problem, or making this change does not solve your problem, visit the post by Amit which tells you how to Stay Logged in With Firefox.