Does it offer you to save them?

Yes, it asks for password update. I select 'Update'.

However the update is never happen. And when I try to log in once again, the password manager enters my old login/password data

Have you tried deleting the saved username and old password from the password manager, then log into the site with the username and new password and saving it that way?

Yes, I've tried this and now it works.

Probably, I've found the reason. One site 'http://editorialmanager.com/' is used by different journal to deal with a manuscript submissions. For different journal's they require a different login/password pair.

For example, for journal1 I have login1 and password1. However, I used the same login 'login1' and different password 'password2' for the second journal.

FIrefox identifies which login/password pair to use only from the site address and login. In my case the login and site address were the same. Journal1: https://www.editorialmanager.com/exif/ Journal2: https://www.editorialmanager.com/something-else/

Firefox decided that these two addresses are the same and could not properly deal with login/password pairs.

I have this problem as well, in Firefox 57.0.1 on a MacBook Pro running Mac OS 10.13.2. I have tried deleting the saved username and password from the list but this does NOT work - the old password is still the first one tried when visiting that site, even though the only login that shows in the list for that site has the new password. It is not that the URL for the login page is slightly different from the one under which the login is saved, because I have searched the entire list and that login is NOT in the list - but it pops up every time I visit that site.

Any ideas about where this "hidden" login might be saved? I do not want to have to delete all of my saved passwords just to get rid of this one, but I may have to as the site will freeze my account after 3 consecutive failed logins.