By default, backups for OneNote notebooks are note enabled. If you want your OneNote notebooks backed up, you must enable the backup in the desired service.
Click Services from the left navigation pane.
Click Microsoft Office 365.
Under Manage Services, click the backup settings icon next to the service that you need to update.
OneNote backups are available for
A list of your backup settings available for the selected service is displayed.
Select ENABLE ONENOTE BACKUP.
Notebooks will be included in the next scheduled backup. If you want them backed up immediately, perform an immediate backup.