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 to log you in automatically.
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.
If that "remember me" cookie is removed or gets corrupted or is not send to the server then the server won't remember you anymore and you need to sign in once again.

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

Some web sites have a way to turn off auto-fill for passwords.

Thanks for the responses. Sorry if my question was unclear. I think I was trying to be too succinct.

No, I mean that, for instance, when I visit a site (for example, my online banking site) where I have no wish whatsoever for my password to be remembered, and I enter my info, I'm either prompted to have FF remember my password or not (and choose Never for this site) or am not prompted at all. Then, hours later, after logging out correctly, I return to the site only to find my username / account number and password auto-filled into the appropriate fields so that anyone using my computer could automatically log in to the site without my consent/assistance.

When I try to remove the information by editing the site in the saved passwords list, the sites are not listed at all.

This has happened on 3 different sites (including this one) in the last 2 days.

Gotta run to work. Hoping that makes sense and thanks again.

Firefox Options > Security. Make sure the Save Passwords option is turned off. Check your add-ons for any that help the password manager.