This isn’t a problem that reinstalling will fix, it appears to be a bug with iOS 13, and Patterning 1 isn’t fully supported on iOS 13. (Export does work in Patterning 2, but that has a different audio engine)
Backing up the database saves the database to the Files app folder (formerly known as iTunes File Sharing folder) for Patterning. When you export the database it gives you a warning message about where the file gets save to. Unfortunately, that folder will be deleted if you delete the app. I’m really sorry about that confusion and that that happened.
Have you recently backed up the entire iPad to iTunes? The database should still be in there if you’ve back the iPad up.
You should be able to use the free (but kind of awful) app iExplorer to navigate iPad backups without needing to restore the entire iPad.