I didn't see any Norton Related applications or products in your system details but I just want to verify if you are using a Norton product on your PC?

Resetting FF generally fixes most issues (keeps bookmarks & passwords) Try resetting FF as indicated below to see if this fixes the problem. It could have been something got checked, altered etc. at sometime for whatever reason.

Please see the following:

Refresh Firefox - reset add-ons and settings

Thank you for the response. I do indeed use Norton and it seems this seems to be part of the issue. I reset Firefox as suggested but as soon as I enable the extension "Norton Toolbar 2012.5.10.1" the "Remember passwords for site" becomes checked but grayed out. After that it is not possible to uncheck it.

I presume from your comments that this is a known Norton issue? Are you aware of a fix?

See:

• http://community.norton.com/t5/Norton-Toolbar-Norton-Identity/NIS-2013-Norton-Toolbar-Unselects-Firefox-Remember-Passwords/td-p/836598

Frustrating - no reported fix despite this being an issue for more than a year with Norton. :-(