I have been thinking of purchasing a Surface Book and checking to see what problems exist.
I have a Surface Pro 2, 256 Gb SSD, 8 Gb Ram and have experienced the same type of drain with it shutdown. I have also noted, while I have it in shutdown mode, using a Bluetooth Ear Bud for my phone which I also use for the computer, that I quite often get a "Computer Connected" and then some time later, probably 10 to 20 seconds, "Computer Disconnected". Thus, some things are still running while shutdown. After about 5 days of being shutdown, my battery is exhausted. I am up to date on Updates.