Does it simply stop playing at that point (but can be
persuaded to continue playing if you
fast-forward/chapter-skip)?

Or, does it freeze up entirely, and have to be
power-cycled to start working again?

It will not fast forward or do anything within the current
file, but I can make it skip to the next file and start
playing it.

It may be that there's something wrong with the files. I'm
working on that possibility. I hope that's it.