Fixed with one button press - stupid simple

If the Wireless Keyboard by Apple disconnects, here is not much help on the internet and Apple's help talks a lot about how it should work, but not, if assistants fail.
Here's what worked for me.
Disclaimer: This is a method I found out trying while not being an apple certified engineer. You do this on Your own risk.

[@josedelrio2190]

That"s cool

[@izperehoda]

"re-pair", huh? Nice wordplay.