Password Resets - infinite loop

What's going on with Apple logins? I get stuck into an infinite loop. I have to keep changing my password. I go round and round with changing passwords, 2 factor authentication. reverification, etc. Since I can't see what I've just typed in, I don't know if it's a typo or some crazy new algorithm. I just give up and use a non-Apple application.

[Edited by Moderator]