I have the same problem. I got a warranty replacement and that process took so long that I bought a different laptop. This was my first non-MBP in a decade and I wanted to love it so badly. After 3 weeks of back-and-forth with Microsoft I had to buy a replacement laptop, and I went back to what I knew.
So when this one finally got to me, I turned it on to check that it worked and then turned it off with a full charge. It has sat for a couple weeks and I recently turned it on take pictures to sell it and it was completely dead. 0% | 0%.
I will never in my life purchase another Surface Book product.
This doesn't really surprise me but just to confirm, you shut it down from the start menu not the power button which depending on your settings might have just put it to sleep. Sleep in Windows 10 uses a lot of power.