Quit from all Mac Office Applications, except for OneNote Sometimes your credentials can get corrupted, causing OneNote to continually prompt you to enter your password.

To clear your Office credentials for macOS If you are still experiencing the issue after installing the recent updates, the next step would be to clear your Office credentials, and recreate them by following these steps: If you also have other Microsoft Office apps for iOS (Word, Excel, PowerPoint, Outlook), you will need to update all of them. To download the latest version of OneNote for iPhone and iPad, check the App Store for automatic updates. To learn more, see Check for updates in OneNote 2016 for Mac. Update all of the Microsoft Office applications, since they all use the same keychain items. If you installed OneNote as part of Microsoft Office for Mac, then open OneNote, go to the Help > Check for Updates menu to launch the Microsoft AutoUpdate app and follow instructions there. You should see the option to update OneNote there. If you've downloaded OneNote from the Mac App Store, launch the App Store and check for Updates. Please update to the latest version of OneNote for Mac, iPhone and iPad. Similarly, OneNote may require you to sign in repeatedly to resolve sync errors.

If you use OneNote 2016 for Mac and OneNote for iPhone and iPad, you may be asked to sign in any time you open the OneNote app or when you switch between notebooks.

Office mac keeps asking for password