Wow, thanks for discussing my question ("[09:53] Surface Type Cover is touchy")!
The weird thing is that we're all having this problem with different keyboards (Touch- and Type Cover). So far I haven't met a single person that hasn't had this problem. All updates, including optional, are installed. Anand Lal Shimpi even mentioned the problem in his recent review of the Surface Pro 3:
"There are also times when the keyboard and/or trackpad will stop responding. In some situations only certain aspects of the Type Cover won't work. For example right now I can't seem to get two finger scrolling or any other trackpad gestures to work. This is a problem I've seen on every single Surface since its release, although the problem itself seems to have gotten better over the years. Thankfully unlike previous implementations, detaching/reattaching the cover is usually enough to fix things."
-- From http://www.anandtech.com/show/8077/microsoft-surface-pro-3-review/2
In the end it seems that we have to live with this part of the Surface experience...