Att email in password loop

ATT changed email password settings. Email accounts that have been setup and working for over 10+years are now in a authentication password loop!? I can use a web browser IE, Chrome and log into yahoo.com - mail - username/email address - password and it works. But when using Safari or Apple Mail, the screen asks for username/email address - password, A screen asking to change the password appears, I enter the correct password and the screen goes back to username/email address. FRUSTRATING.