After months of trying to figure out why my RP3 system would fail to update, I finally got to the bottom of the problem with pvizeli.
When you request an Update, the RP3 system performs extended flash writes. The power supply that came with my RP3 system is insufficiently sized to supply the power required to perform these writes. The system would simply reset and come back with the same hass.io version that I started with. So I swapped out the power supply for a larger one and voila, updates now work!
Some folks thought perhaps the flash card manufacturer was an issue, but it’s probably more likely that some manufacturers require more power to flash than others. So, anyone having difficulties upgrading hass.io from an RPI, try a better power supply. The power supply that failed to update was rated at 0.7 A, 5 V and the power supply that works like charm is rated at 1.0 A, 5 V.