Sounds like a bug in the app, maybe a delay before notations are saved. I'd check with the developer site and/or comments in the App Store to see if it is a common problem.
Here are a few things you can try, experimentally.
1) Instead of leaving the notation mode, close the app. This should force a save if the app is working correctly.
2) Wait a a few minutes before closing the notation mode. Maybe the app isn't saving as often as it should. Badly written if it has any delay in saving, but who knows.
3) Look for an Save option in the app. If it exists you can force a save. This is rarely needed in iPad apps, but some apps developed for other platforms then ported to iPadOS have explicit Save options.
4) Make certain you are using the most current version of the app. If you are lucky this bug has already been fixed.
That is all I can think off.