Suddenly my Android Wear smartwatch LG-W200A Watch Urbane 2nd Edition LTE seemed completely dead. It had 80% battery charge, I set it down on the desk and say an hour later I noticed it wouldn’t respond to any buttons or screen press. There was zero current draw when connected to the factory charger (as tested with a USB power meter).
After several hours passed, I was processing the warranty claim form, and pulled the SIM out. After another twenty minutes or so, I heard a long ~ 1 second vibrator buzz from the watch, and suddenly the watch responded to the center circle button press, saying the SIM had been removed, and that the battery was low with 15% remaining. It also said “Android Wear is not responding” and I clicked OK to end (restart) the task.
I suspect what woke the watch was getting to low 15% battery. It took probably 6 hours to go from 80% to 15% (normally the LG Watch Urbane 2nd Edition LTE battery lasts 2-3 days).
So if your Android Wear smartwatch suddenly stops responding to all button presses and you know it was charged or try charging it with no response, consider letting it sit disconnected from the charger for 1-2 days to allow the battery to run out, then apply the charger again. In a few seconds you should see the screen come on.