You could try clearing all your cookies. I remember once one of the cookies in my browser became corrupt. No matter what it would never save anything. Once I cleared everything, it seemed to work again. Clearing cookies can be annoying but you can have Firefox remember all your accounts/passwords in the future. As long as you own the computer (not a university one), it should be fine. Just remember never to save logins for important things like online banking. Just keep those logins in your head.
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