Some updates:
I just had my Type Cover driver disappearing again with my Surface Pro 4.
Same as previously - nothing helped until I whipped out my old Type Cover and connected that - voila it did again the trick and re-installed the driver and both type covers work again.
I have not seen this on my Surface Pro 3 or Surface Pro 6 - both are using the same type cover (the grey alcantara one).
The Surface Pro 4 worked just fine for a few months - with carrying around detaching the cover a few times, hibernating etc.
So - whatever happened with the latest updates (I got already build 1903 on all my Surfaces) the issue re-appeared.
I don't know what I would have done without my old type cover that seems to "reset" the connection and gets the driver installed again.
Hope this helps someone....
Cheers,
Ralf