Here is a list of things you should do if OneNote is not saving changes to a local notebook in OneNote for Mac:

1. Check that your OneNote local notebook is properly connected and synced by signing in with your Microsoft account.
2. Check that you have the most current version of OneNote.
3. Update macOS to the most recent version available.
4. Launch OneNote to ensure the changes are processed and saved in the local notebook.
5. Restart your Mac.
6. Back up all of your OneNote notebook data to a different storage location as a preventive measure in case of future data loss.
7. Uninstall OneNote and reinstall it.