From the descripton in the first post, your cookies might be set to be deleted when you close FireFox. Cookies are needed to stay logged in.
If you wish to stay logged in after closing FireFox, and starting it again, you can change the settings:
Tools -> Options -> Privacy
Then there is a "Settings" button next to "clear history when FireFox closes". Click on that "Settings" button, and uncheck "Cookies".
Does this help?
(I personally let FireFox delete my history and cookies when I close it for security reasons, and prefer to log in again when I restart FireFox.)
Edited by Mysterysgames, 19 July 2009 - 06:18 PM.