Hello @Rajeeb Das,
Thank you for reaching out to the Quicken Community, though I do apologize that you are experiencing this issue.
To clarify, you are attempting to run a One Step Update yet are being repeatedly prompted to input your passwords for your American Express accounts?
If so, I suggest you try signing out of your data file completely and then signing back in to refresh the registration token for your Online Connected Services. However, I do recommend that you first save a backup file prior to performing these steps.
Please let me know how this goes!