Does it make you log back in? Or does it forget the Auto Fill in part? If you have to log back in everytime, it means that IE9 is dumping your cookies. I am not sure if you are familiar with browsers, but cookies are small pieces of data stored in your browser, telling the website your identity, so you are "remembered" for next time. IE9 might be set to dump browsing history and cookies every time you close your browser. Your settings can also be configured to not accept any cookies, which won't allow the "remember me" function to work.
The other issue is the Auto Fill or Auto Complete, (whatever IE9 calls it, it's different name for every browser.) I have this happen to me all the time. I have IE9 set to remember forms, username and passwords, and sometimes, it won't automatically fill in my credentials when I select the username or password box on websites. This is a common issue with IE I think.