You can find out what session the browser was using before the logout event and then see if it still exists or is corrupted in some way after the logout event. For Firefox, open the storage inspector with shift F9. The session name is stored as a cookie. After the unexpected logout, look for the session file on the server. If it is gone, then you know that something on the server removed it.
If it is still there, then the problem becomes more interesting, as then you will need to examine the file for clues why FA could not use it. I would also guess that if it were still there, FA would display "authorization timeout" or some other error message.
Note that when a session file is removed unexpectedly, FA will initiate a logout and create a new session. So looking for the session cookie name after logout tells you nothing. FA apparently does not issue an error message if its cookie is gone. The screen display is the same as when a brand new session is initiated with FA.