PROBLEM: Every time you want to access a password protected site, you have to login even though you checked the box to remember your login.
SOLUTION: Type ABOUT:CONFIG in the address bar and then press enter to accept the warning. Do a search for network.cookie.cookieBehavior and change the integer to zero.
WHY: Probably due to security concerns. I guess it is safer to default to logging in every time rather than all passwords being saved no matter where you are.
NOTE: Your browser will ALWAYS show HTTPS regardless of this setting. Messing around with about:config can seriously damage your browser. Do this only if you know what you are doing or can follow instructions.