Seems like this may we widespread. I am having the same issues and my watch is only 4 months old. T-Mobile is replacing this for $20 (which I am not a fan of paying).
I wonder how many units have reported this behavior?
If it's in warranty which it should be in since the watch released in nov last year just call or chat Samsung and I sent off mine to get fixed. It's completely free but takes two weeks.
My watch battery goes low and powered off, after charging, I hold power bottom about 15 seconds, suddenly turned on and then power/home bottom work perfect like before!
But after few minutes its stop working!
At first I thought that its a hardware failure, but seems that was os bug.