You may be in the incorrect Amazon password loop that makes no sense until you know the trick.
Set a secure password.
You click the forgot password button to trigger the authentication to your email or phone, that all goes well, and then you set a nice memorable password. You do the same for the other Amazon account; for example, you have amazon.com and amazon.co.uk, or you are an Amazon affiliate and need to update your affiliate password simultaneously.
This is when you get into the incorrect password loop because although the password initially works and allows you to log in, the password fails on subsequent attempts to log into Amazon,
It is impossible to have a password for each of the domains associated with your Amazon accounts. Good practice would suggest different passwords for each domain to provide a separation should a password be breached/guessed/phished.
I can only get all my different Amazon domain logins to work with a single password. Whichever I update last becomes the master password for all the Amazon domains I try to log into. I got into a loop of setting a password, testing it, and then setting another one on a different Amazon site that overrides the previous one—effectively forcing me to use the same password over multiple Amazon domains.
That little gem wasted 20 minutes checking, saving, and testing passwords several times over several Amazon domains. I suppose it is for convenience, but it needs to be backed up with a 2FA - The second factor of authentication like an SMS message, app notification, or old-fashioned email.