Do you mean names and passwords in the Password Manager or do you mean that you are no longer logged on to (remembered by) websites after closing and restarting Firefox?
There is a difference between remembering the name and password in the Password Manager and a "remember me" check box on a web page.
The latter usually involves the creation of a special "remember me" cookie that is stored on your computer and that is send to the server.

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.
• In Private Browsing - Use Firefox without saving history mode Firefox won't fill names and passwords automatically and won't offer to store new passwords.

• 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

Hi cor-el

Thanks a lot , it worked well. I opted for "Never remember history", noe I changed to "remember history" that solved my problem.

Have a great day!!

In my case passwords are saved, but not are displayed in Options>safety>Saved passwords  : the window opened it's completelly clear (see uploaded image)

I have installed "password Exporter 1.2.1" extension. When I run this extension, a correct file xml with passwords is created. And passwords are correctly saved, but is not possible to see.

(Sorry for my poor english)

potxo