Doubleshot stock is loose or wiggles
If the stock screw is tight, the stock will not wiggle. The first thing to try is to get in there and tighten it more until it stops wiggling.
It is also possible that the rod is not screwed into the receiver all of the way and the nut is bottoming out on the threads. Pull the stock all of the way off and then turn the rod into the receiver, allowing more threads for the nut to tighten down on.