Some sites like PayPal, Yahoo, Windows Live and bank sites use autocomplete="off" to prevent Firefox from saving and filling the name and the password.

If a site uses autocomplete="off" then look at this article for a bookmarklet to remove that autocomplete attribute and Firefox will offer to store the name and password.

• http://kb.mozillazine.org/User_name_and_password_not_remembered (bookmarklet)
• http://kb.mozillazine.org/Password_Manager
• http://en.wikipedia.org/wiki/Bookmarklet

I should have been more specific in my question. Can you get Firefox to prompt you to remember the password for a specific website when you have previously (accidentally) told Firefox not to remember the password for that site?

If you clicked "Never" then you have created an exception that you need to remove.

Remove site(s) from the Exceptions:

• Tools > Options > Security: Passwords: Exceptions

• http://kb.mozillazine.org/Password_Manager

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 Firefox won't fill names and passwords automatically and won't offer to store new passwords.

Thanks a lot for solving my problem!

You're welcome