This is not currently possible (unless you have a special program on your computer that allows you to access all the files on your connected smartphone.) The simple MIDI tunes are mainly intended to just be a reference so users know what the song sounds like.

We appreciate your kind words! We have lots more hymns coming in the near and more distant future.

You must be experiencing a device specific problem. The app is designed to retain downloads until the user deletes them. We are not able to replicate your problem and have no reports of this happening to other users. Try deleting and reinstalling the most recent version of the app.

As no other users have reported a similar issue or voted for this one, we have judged this as an isolated incident specific to an individual user and is being closed.