First of all, it doesn't matter whether if you have saved your e-mail address and its password on your PC. It's meant for your WLMsgr so that each time you want to sign in, there's already the saved e-mail and password for you to log in with ease.
Second of all, did check
Always ask me for my password when checking Hotmail or opening other Microsoft Passport enabled web page or is it unchecked?
Third of all, how long did you set your
session expiration in your Hotmail?
Last but not least, did you enable cookies on your browser?