I've been having this issue since I got my Surface Pro 3 a few months ago. It will be charged to 100% when I shut it down from the power options on the start screen. When I come to turn it on the next day (less than 24 hours later) it shows the empty battery icon on screen and won't turn on. When I plug it into the mains it turns on and I find that the battery has been drained to 5-6%. I primarily use it in a docking station and rarely charge it with the adapter. Not sure if this has anything to do with it? Other than that it seems to be pretty random when it happens. Most of the time it will still have over 95% charge when I come to use it the next day.