Here is a list of things you can do to help fix OneNote not saving changes to a shared notebook on a Mac:

1. Make sure you are using the latest version of OneNote
2. Quit and restart OneNote on your Mac
3. Sign out of Office and OneNote and then sign in again
4. Uninstall Office for Mac and then reinstall it
5. Check your Internet connection
6. Disable third-party antivirus to check if it is causing the issue