Cookies must be enabled in your browser to Login, and remember your Login.
Accept cookies until they expire.
Make sure your browser is not clearing cookies on exit (Firefox private data).
If you don't like keeping all cookies, Firefox users can install an Add-On called SelectiveCookieDelete. This can keep (white-list) or delete (black-list) selected cookies when the browser exits.
On some browsers, you can disable cookies then add an exception for only this website.
If you're just trying to remember your password (and not your login), this option must be enabled in your browser, not cleared on exit, and you must click OK when prompted to "remember this password".