Follow up: I did have the issue again. I think it's a connection issue with the sim. I took the tray out, physically bent it just a little to angle the tray DOWN in an attempt to improve the contact of the sim with the phone. It seems to have worked as I haven't had an issue since.
The tray is made of a very durable metal so bending it is very hard. The bend I made is not noticeable, but I notice that when inserted it sits slightly different along the edge. That tiny bit of extra pressure connecting the phone with the sim seems to have corrected it.
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Device: HTC One M8 (VZW)
Retired Devices: Samsung Galaxy S III (VZW), HTC Droid Incredible