This recently happened to me. After the latest software update, not sure of rev, my Gear seemed to not charge right. Then while on vacation it quit charging completely.
Ended up completely draining the battery so it would do nothing.
Just got it working again last night. I had to take off the back and clean the contacts between the back and the main board. After doing that and re-assembling the Gear charged fine. I let it sit on the charger overnight (was at 73% when I went to bed). This morning it was at 100% and I'm sitting at 86% now (9hrs later).
It appears that there was a little corrosion between the contacts and the rear of the watch that contains the wiring to magnetically charge the battery was giving too much resistance (or possibly open circuit) so the battery couldn't get a charge.
I may still need a new battery; will keep my eye on the usage rate over the next week or so. But I'm happy to have my Gear back in operation.