I use BSI most of the time, but it wasn't until I couldn't access it that I realized how much I also use the onscreen keyboard. I reported the issue to Apple, and at their request, I sent them a screenshot of the keyboard not popping up.
I've tried turning off bluetooth, I've tried double-tapping and holding, and everything else that folks have suggested so far. I'm open to new suggestions if anyone has any.
Thanks, and I'll let you know what Apple comes up with.