I tried turning off cellular data while listening to a podcast during a >30 min walk and it didn't shut down. It shut down after I got home and toggled the radio back on. There may be something to the cell network switching hypothesis.
Mine dies almost every night, though I can't remember if it's face up or down. I guess it wouldn't matter much to the sensor since it's pitch black either way. Mine doesn't shut off when plugged into an AC source, but given that that implies little if any cell-tower handoff (but shutting off overnight doesn't make a lot of sense in that case).
That said, if you're moving around while it's plugged into a mobile DC source, while having cell towers hand it off, and it's still not shutting down, that could be a clue.