When using OneNote on an iPad does it store anything locally? I thought it required OneDrive or some cloud storage location to even begin using the app. That being said I've run into a scenario where a user claims to have updated a OneNote file on his iPad, but the changes weren't syncing to OneDrive and therefore were not visiable on his desktop client. He then started having trouble accessing OneNote on the iPad at all so I had him delete the app and download it again. This allowed him to access, but the changes that were only on his iPad were lost. How's that even possible if it doesn't store anything locally?
Wouldn't it make sense for OneNote to keep a local 'cache' of it's content on the device? This is what it should probably do in the event a user is working offline (OneNote can be used in Offline mode).
Then, if for any reason, there are syncing errors preventing local changes from going 'up' into the cloud, you would experience the things mentioned. Deleting the app deletes it's local content.