I also started getting this authentication prompt on my websites which contain advertisements from Google AdSense. It seems that only some ads cause this prompt to appear.
The issue was fixed by signing out of all of my Google accounts from the main Google site (https://www.google.com/) I am no longer receiving the authentication prompt even after logging back into the accounts.
None of my several hundred active users are reporting the prompt, so I believe the issue was affecting me because my account was signed into Google AdSense.