Liatris are susceptable to root rot and stress makes them more vulnerable. Various fungi in the soil are the culprits- I think Liatris is commonly affected by the rhizoctonia fungi which is the same bugger that goes after my iris rhizomes. This would be my stab in the dark guess- particularily for the first plant. If this is what you have then there isn't much you can do to help them other than letting them dry out and hope they can fight it off themselves. Iris growers sometimes dig up the rhizome and cut off the rotted part and sprinkle them with an antifungal powder before replanting them in new soil.
Others may have other suggestions for what your problem is. Don't get bummed out- obviously you can grow these successfully and it may just be a season's setback.

I'd agree with the fungal problem. Both germanic iris and liatris seem to like things a bit on the dry sunny side. If they're too moist, soil fungi can really get at them. Sandy or elevated sites without heavy mulch might be the best bet--good luck!