In general, the problem seems to be that the Response Properties checkbox in the Screen Options (in the top right hand corner of the admin UI) doesn’t seem to remember its prior state. Thus I’ve needed to occasionally open the screen options and recheck the Response Properties box to see its meta box.
I’ve played around with it a bit, but can’t always reliably recreate the issue. It does seem to be happening less frequently now compared to when I originally upgraded. Is it possible that the checkbox state is only saved per kind?