Just to provide my experience on this.
Surface Pro 4.
I am now typing this reply on my type cover. On one of two of my type covers that had stopped working after an update that I couldn't roll back.
Tried all the usual suggested stuff, contact cleaning, hard restarts, uninstalling drivers etc, preforming all updates.
My symptoms were the following.
Surface Type cover filter not showing in device manager.
when I would connect my type cover the screen would turn off, no keys or back lights would work, touch screen would not work. Interestingly the machine was still operational, I could vnc in.
Type cover would not work at all in UEFI.
Reading on these forums last night that upgrading on the insider programme to build 18362 had solved the issue for some people.
I signed up and installed the download, restarted and logged in (all with no type cover connected).
Once logged in I connected a cover and now it appears to be working flawlessly.
Note that I haven't switched off the screen, put it to sleep, closed the cover, rebooted or removed the type cover yet. If it stops working I'll update this post.