If you are using a new Surface Book, or Surface Pro 4 make sure you go and check Windows Update. Each device is now receiving a System hardware update: 12/17/15 to help make their keyboards work better.

Unfortunately, neither of these updates appear to address the battery drainage issue associated with Connected Standby. However, there are some brief changelogs for each, and they seem to fix issues when removing the Type Cover and typing on the Surface Book.