Unless you share your computer with anyone, logging out is really not neccessary. If you do share your computer I wouldn’t automatically log in, either.
My problem is that my password shows up in the password field so anybody can log in on my PC under my name and I can’t remove it from the field. I would like to input my password each time I log in rather than have it already in the password field. I do not have the automatic feature selected. Changing the password did not correct the problem either.
Another possibility - the other day I was having browser problems and had to delete my history and all cookies. As a result, when next visited FAOL, I was not logged in automatically. Might want to look at your browser settings and see if you have cookies enabled?