Before you hit Enter for the password thy running the "Remember Password" bookmarklet which you can give a keyword shortcut of "Remember:" to make it easier to use. If it does anything you will see messages that it removed some items from forms.

ignore website requests to not remember password -- http://www.squarefree.com/bookmarklets/forms.html#remember_password

You may see a yellow band across the top asking you if you want to save the password, you would answer that in order to save.

It is possible that there is a problem with the files key3.db and signons.sqlite that store the encrypted names and passwords in Firefox.
Rename the files key3.db and signons.sqlite in the Firefox profile folder.
You can add .old to the file names (key3.db.old and signons.sqlite.old) or move them to another folder to make it possible to undo the action.
You need to set a new Master Password after renaming or deleting key3.db and all currently saved passwords are lost.
If that has worked then you can remove the renamed files that are no longer needed.

See:

• "Troubleshooting" in http://kb.mozillazine.org/Password_Manager

• Password Exporter - https://addons.mozilla.org/firefox/addon/password-exporter/