Here are some steps to try if your OneNote local notebook isn’t saving your changes:

1. Check your internet connection: Make sure you are connected to the internet and that it is stable.
2. Force sync: You can try to force OneNote to sync changes by pressing the sync now option, which can be found under the File tab.
3. Close and reopen OneNote: Close and reopen OneNote and try to save your changes again.
4. Restart your computer: Restarting your computer can sometimes fix the issue.
5. Check if you have the latest update of OneNote: You can check for updates and install them manually by clicking on Tools and then Check for updates.
6. Create a new notebook: If all the steps above fail, you can try to create a new notebook and save your changes in it.