Ok, I think I've come closer to identifying the culprit, but don't know a solution yet.

If I start a new song file, type in chords, and play the style, the pedal steel plays all the way through. Adding the audio track later doesn't mess anything up either.

But if I start a new file, and instead of typing chords, I import them from an existing midi file, the pedal steel will only play one or two notes in the first bar and then stop playing.

My guess is that perhaps I have got some setting in the
[File / Import Chords from MIDI file]
dialogue wrong -- but wow there are so many... any ideas what I should try?