I found what might be the problem. Here are two files I have copied to the Android --
One is the .flac music file, the other is a .cue file for indexing the tracks in it.
Next, I have a .m3u file that looks like this -
#EXTINF:1348, Johann Sebastian Bach - English Suite for Keyboard No. 1 in A Major, BWV 806
(it has more in it than that, I'm just showing the relevant parts) This playlist cannot be processed by Poweramp. It says "Looks like nothing to me." The .cue file can be played by selecting it directly, and so can the .flac file. But the playlist file is a no-go.
I've been using .m3u files in PA for ages and have never run into this; maybe I never noticed? But the error behavior is 100% consistent on other playlists that refer to files that have the same naming convention (name.flac + name.flac.cue).
btw, this convention is a leftover artifact of using Total Recorder to generate the .cue files. I will attempt to remove the .flac part of the .cue filename and see if that makes PA any happier. Also btw, I have done a full rescan and it still occurs.
Thanks for the hint, Andre.