I realise it's many years since you posted this, but I have just found it and have an ongoing issue that this might help with.
When windows runs updates, or, if I accidentally put my surface pro 3 into sleep mode, the Surface Type Cover gets toggled off, and does not toggle back on when restarted, or awakened from sleep. I usually the go through a weeks long episodes of on-of cycles, uninstalling updates, resets and restarts, driver deletions and re-installations until I can get it working again. There never seems to be one consistent way to get it working. For years I had automatic updates off because every time it would disable the type cover keyboard.
I have recently seen that newer surface devices have a toggle switch available through the UEFI (https://support.microsoft.com/en-us/surface/troubleshoot-surface-type-cover-or-keyboard-c106b37d-f55a-4640-8cb2-8f1b2b0207ea) but there isn't one on my Surface Pro 3 (even though its a Pro device). Trying to find it is is what brought me to here ... So is it possible to toggle the Type cover through this Powershell option? Because recently ( I mean 3 weeks ago) it happened again I'm still trying to solve it.