Of course, it doesn't!!! Imagine if someone uses your Firefox session and is able to connect to your online bank account without your permission? Some websites can report to the browsers to not save the login/password locally (with a special attribute in HTML forms).

Thanks for the quick reply. I understand your security concerns. But as with my old bank's website (that bank was bought by new bank), FF retained my user ID, thereby making logging in quicker and simpler. Would like to duplicate that ease of logging in. I asked the new bank's help desk and they seem to think it is a FF problem since they say it works with others.

Is it possible to provide the link to your bank's website? I will tell you if it's possible or not to save your login/pwd.

Sure thing

Thanks, but that's what I told, the form forbids to save the data: <form autocomplete="off">.

When autocomplete is off, FF is not able to store the login/password. You can force Firefox to autocomplete but it's at your own risks, see http://www.techzilo.com/force-auto-complete-fill-forms-firefox/ (or search on Google).