@malikzeeb Hi - in Windows the saved passwords are encrypted using a key from your OS login session (DPAPI) as well as a secret in a browser file (Local State). If this somehow fails, for instance if you change user account or the secret somehow gets deleted, decryption will fail.
The password for Sync is stored like regular passwords in the browser.
When this happens, do:
Check Settings > Privacy > Passwords > Show saved passwords. Make sure there's an entry for vivaldi://settings/sync and that you can view it (click the eye icon).
Check the Chromium internal chrome://password-manager/passwords for the same.
You will be prompted for your OS user password to view the passwords.
Also try using the tool WebBrowserPassView to view your passwords:
https://www.nirsoft.net/utils/web_browser_password.html
This should automatically find Vivaldi's login data file and decrypt the passwords. It's a good way to find if the password decryption is working as expected and/or if you've got duplicates messing things up.
The only reason I can think of that your would be asked repeatedly for your Sync password is if the browser is somehow unable to decrypt it. As to the why this happens, no good idea, could be external "security" tools on your system, or maybe an extension.