It was working well before. I don't think I'm doing anything different.
(Note that Pro Microphone will spam you mercilessly unless you shell out nineteen clams.)
It did save just one track that I used for a sound check. But when I tried twice singing complete songs, despite that the UI said "Your File Has Been Saved" after I stopped these two recordings, the files were not saved.
Music Paradise, the App's publisher, did not respond to any of my previous Support Requests. EDIT: That's because their mail bounces!