iCloud keep asking for old Apple ID Password

icloud keeps asking for password for old email address. When I say forgot, it states old email address is not supported. then when I put in my new Apple id and say forgot password, I have to change password. I have changed password 5 or 6 times. When icloud comes back up, it asks for the password for the old email address again. Viscious cycle. I have updated all information for my Apple id. Does anyone know how to get rid of old email address in icloud?