Start Firefox in Safe Mode {web Link} by holding down the <Shift>
(Mac=Options) key, and then starting Firefox. Is the problem still there?

Look on your desktop. Do you see a folder called; Old Firefox?

https://support.mozilla.org/en-US/kb/recovering-important-data-from-an-old-profile

https://support.mozilla.org/en-US/kb/back-and-restore-information-firefox-profiles

In the event that the passwords information is lost, you should record all information in a separate text file somewhere else on your hard drive, or written down. You can easily copy and paste if you need to do so. If you are concerned about someone else looking at that file, you can compress it using a password.

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 this "remember me" cookie is removed or gets corrupted or is not send to the server then the server won't remember you and you will have to sign in once again. You can remove this "remember me" cookie to make the website forget you and require you to sign in again.