It's probably one of two things -- dried up foliage from the heat and dry weather we had earlier -- or fungus from the wet we've had recently. I've had all sorts of aster in Chicago, and the same ones now in Kansas, and they just don't do as well in Kansas. But they do better if you shear them back two or three times (by about a third) before mid-July. then they don't flop and expose the center and two feet of ugly leafless brown stems.

If you could post a picture, that would help, but there is no point keeping moldy or dried plant parts, so cut them off.