There is a difference between remembering the name and password in the Password Manager and a "remember me" check box on a web page.

Websites remembering you and automatically log you in is stored in a cookie.

• Create an allow cookie exception (Tools > Options > Privacy > Cookies: Exceptions) to keep such a cookie, especially for secure websites and if cookies expire when Firefox is closed.

Make sure that you do not run Firefox in Private Browsing mode.

• https://support.mozilla.com/kb/Private+Browsing
• In Private Browsing - Use Firefox without saving history mode all cookies are session cookies that expire if that session is ended, so websites won't remember you.

• Do not use Delete browsing, search and download history on Firefox to clear the "Cookies" and the "Site Preferences"

Clearing "Site Preferences" clears all exceptions for cookies, images, pop-up windows, software installation, and passwords.

• http://kb.mozillazine.org/Cookies

• Press F10 or tap the Alt key to bring up the "Menu Bar" temporarily if the Menu Bar is hidden.
• Use "Firefox > Options" instead of "Tools > Options" if the menu bar is hidden.

If you can access your password manager tools/options/security/saved passwords, then look at the URL that your password manager says it is trying to connect to and compare it to the website that you are actually trying to connect to. Something has changed in the new Firefox release and the URL you are trying to access with the password manager NOW needs to be exactly the same as in the manager.

I have been using https://www.google.com as the gmail password manager page - for like forever. Suddenly the Firefox Password manager now needs https://accounts.google.com to function. Either Gmail just changed or Firefox changed.