I've finally figured out what is going on. At some point, the users had turned off compass calibration in their location privacy settings. And since my apps are set to request calibrated data, the app gets no compass data at all.
So, to fix, open the iOS Settings app.
Tap the System Services item (way down on the bottom):
If Compass Calibration is disabled, then this was likely your problem. Enable it.
I should look into detecting this condition and warning the user. Hope this helps.