This has never happened to me. When you log on, as in, when you type in your password & user name, does a small box come up on your screen and say 'Would you like The Internet to remember you?'? If not, it's a glitch. If the window does come up, click the box inside of the pop-up that says 'Never ask me this again' and click Yes.
That has happened to me also. I think that it auto logs off because of opening and closing the window for AG. this happens to me after 5 or 6 times opening and closing AG.