Remember the password manager just auto fills the password field, its the cookies that keep your session with XYZ site logged in.
Sounds like a cookie problem to me.
Short Answer: do disk cleanup, deleted temp internet files, reinstall FF.
Long Answer: make sure the cookies for whatever site its happening on are not creating new unique cookies every time you visit. If they are, maybe try dropping the security for that site or add it to a whitelist depending on the software you're using. Are you part of a windows domain? If so, use gpedit to check domain settings for the internet, otherwise check your folder permissions and that FF has modify permissions for cookies it creates (admittedly a long shot). Its also possible its the site, not your browser, but this is unlikely. Without mroe info on your setup, kinda hard to tell.
Good work switching to FF though, once you've got it working properly, you'll realise that anybody who uses IE for anything other than testing websites to see if they work in IE, is a moron.