I've never found the log off button either.

The following seems to work: When you are ready to log off, manually type in the URL http://www.aa.com

At this point, it will again have a place to log in. I'm not sure if the following step is necessary, but if you are on a public terminal or something, it would be a good idea to "log in" using a non-existent Aadvantage number and PIN.