If you plug the Deck charger into the dock, then plug the Deck and keyboard into the dock, it works, right?
If so, the problem is that the Deck does not provide enough power for both the dock and the keyboard.
I have my charger plugged into the dock 24/7 with no problems.
BTW, buying the official dock may not solve your problem. I have the official dock. When the Deck battery gets low, it does not provide enough power for both the dock and one of my keyboards.