A few things to check:

1. Is the problem seen with only 1 specific site?
2. Does Firefox remember usernames/passwords for other sites?
3. How do other browsers (IE, Chrome etc) behave with this specific site?

There are some websites which do not allow passwords to be saved for security reasons. If you find that the problem is with only 1 site for all browsers, that site may have disabled password saving.

Some web sites tell browsers not to remember passwords by using autocomplete="off" on the login page, which tells the browser not to save the password for that page. This bookmarklet makes the browser ignore autocomplete="off" temporarily, allowing you to save passwords even on sites that use autocomplete="off".

Remember Password bookmarklet:
https://www.squarefree.com/bookmarklets/forms.html#remember_password

Just drag that Bookmarklet in to your bookmarks, toolbar or drop-down list, and click that Bookmarklet like you would click on a bookmark before you you submit your login to the website.

Then, there's the Saved Password Editor extension which has a feature that allows you to manually add new username / passwords to the Saved Passwords window.
https://addons.mozilla.org/en-US/firefox/addon/saved-password-editor/

Your above posted system details shows 2 Flash plugins.

1. Shockwave Flash 10.3 r181
2. Shockwave Flash 10.1 r82

You should remove the older Flash 10.1 r82 plugin version.

• http://kb.mozillazine.org/Issues_related_to_plugins#Identifying_installed_plugins

See also:

• http://kb.mozillazine.org/User_name_and_password_not_remembered