First, let's clear things up: when you save a password in Firefox, it's stored in your computer, and isn't shared or uploaded to anywhere. It's also encrypted so only Firefox can read it (i.e. use it to auto complete passwords), and keep it away from the prying eyes of malware, viruses and whatnot. Saving your password to Firefox is completely safe and that password will only be available to someone who users your Firefox profile. If you want to have different Firefox profiles for different users, please read "http://support.mozilla.com/en-US/kb/Managing+profiles" On the other hand, when you ask a site to "log you in automatically", it has <em>absolutely</em> nothing to do with Firefox's password manager. When you ask a site to always log you in, the sites stores a "http://support.mozilla.com/en-US/kb/Cookies" >cookie</a> in your browser (in this case, Firefox, and not other browsers you may have installed or Firefox in other computers - unless you have them synced with <a href="http://www.mozilla.com/firefox/sync/" that the site will use each time you visit it to know whether your logged in or not. This cookie is exactly the same kind of technology a site uses to know if you're logged in at all. Without cookies (i.e., if you have href="http://support.mozilla.com/en-US/kb/Enabling+and+disabling+cookies"you'll need to be constantly logging in, because the site won't be able to remember that you already did log in. This renders most, if not all, sites that require you to log in completely useless. If you don't want to be always logged in in a given site, simply don't ask it to always log you in. You may need to log out and log in again to tell him that, but that's an usability issue with the site, not with Firefox.

Try clearing your cookies for all Google domains. See this support page / paragraph. https://support.mozilla.org/en-US/kb/delete-cookies-remove-info-websites-stored#w_delete-cookies-for-a-single-site

Thank you for the explanation, but why has the failure to stay logged in to my google accts coincide with the Firefox upgrade. Are you saying that it is completely a problem with my Google accounts?

I suspect that some websites have a problem recognizing cookies that the website set in the previous version of Firefox, hence my recommendation that you clear all your Google cookies and allow those cookies to be set once again.