Outlook can repeatedly ask for a password due to various reasons such as unstable internet connection, cached credentials, outdated version of Outlook, outdated operating system, incorrect email account settings, or add-ins causing issues with Outlook. To resolve the issue, steps such as clearing cached credentials, updating Outlook and the operating system, verifying email account settings, disabling add-ins, and contacting the email service provider for further assistance can be taken.

You can follow this technical article to learn about the reliable methods to fix Outlook keep asking for password. Go for the manual trick but if it does not provide a satisfactory result, use the PST Password Remover Tool. It is developed with advanced algorithms to remove the password of PST files.