How do you mean loose all logins? 2FA work differently then non-2FA logins as 2FA requires something like email authentications or smartphone sms to verify the user. Also Amazon requires if you use different device or computer to verify whom you are before you can login as well. One should 2FA if they know for sure they will not loose their 2FA because if you do that account becomes a "Lost" account and there's no way to restore it. I have "remember me" for my Login and I just verify the correct Login and matching password for Amazon and have no issues when I login. I have yet to see sites trigger Firefox to forget logins beyond the customer "clearing cookies/cache/history" would wipe all logins clear and one has to redo the login or "captcha" to login. And since no one here knows your login sites no one can be sure what exactly is happening if you did set "remember me" options. My only other that comes close to 2FA is google authenticator but that is set on my smartphone so I won't loose it.

By loose login I mean sites where I previously were logged in are now all logged out ... twitter, https://stackoverflow.com , github.com etc ...

This problem is a firefox thing ... no action on any one tab on any site should have the power to force firefox to logout of all sites ... unless I am missing something