We have tested in great depth with firefox (and do compatibility testing with IE, Opera and Safari), but there are a few settings that can get mucked up in firefox.
Posting here is the best place too, as then people who end up with similar problems can read through and figure out what is wrong without PMing back and forth
One thing that seems to be a relatively common firefox problem is your firefox profile getting slightly corrupted, causing unpredictable behaviour. This can happen quite naturally from upgrading firefox between versions, disk failures or crashes, and many other reasons. I sometimes recommend that you try resetting your firefox profile with the instructions provided here:
http://kb.mozillazine.org/Creating_a_new_Firefox_profile_on_Windows
before you do so, please make sure that you have a backup (or list) of all your settings including bookmarks as you will need to re-enter them after setting things up. This will rule out any problems with firefox configuration though.
Your ISP might be unusual and could use a large number of proxy servers that have different IP addresses which will result in the login system getting confused as to where you are coming from and sometimes this will cause you to be logged out for security reasons. Since you have tried it with IE and have not had any problems that can be ruled out in this instance (AOL are the main ISP who do things like that
fwiw).