Thanks for this. Mine wouldn't respond to the button for turning the screen on/off or turning the device on/off. I turned off BT at the Gear Fit several times and did a reset from the settings function several times. Nothing seemed to work and it was down to 1% battery.
I found this forum, turned off BT at the phone and the Fit immediately started charging; all functionality returned as well. Turned BT back on at the phone and everything is fine and working properly!