To stay logged in longer, make sure you have cookies enabled in your browser (Netscape, Explorer, Mozilla, AOL, etc). To do this, look under Tools / Settings / Preferences at the top of the browser window.

If it asks you to change your password, it seems to accept it better and longer if you change your password in your profile instead of the little window that pops up.

Also, older browsers seem to have a harder time with the site so maybe try to download updates.