Why do my dumplings start out airy inside when done,and then get all hard in the middle after they sit?

Answer 1

One thing that comes to my mind is: are you over mixing the dough which will make the gluten in the flour tough (over worked) or maybe you are adding to much flour as you are rolling them and the last: are you sure it is a good recipe to start with and were all the measurements accurate

Answer 2

Besides the overmixing talked about above, it's also possible that the dumplings are just losing their moisture because you took them out of the hot liquid and then set them in a bowl. And they continue to cook for a bit before they start to cool down.

I always put a little of the liquid they've been simmering in onto the top of the dumplings whether it's on the individual plate or in a serving bowl.