Susan, you're correct, they do prefer shallow planting- I cover them with about 1 1/2" of soil and they seem happy. Good to see you posting! Haven't "run into you" for a long time
Caroline, I've usually had a few that won't bloom the first year that typically will bulk up and start blooming the following year. Here they go dormant soon after blooming (they start with late blooming peonies here and bloom for a few weeks afterword). I think that may be the withering you're seeing. Be sure to mark the spot well- I'm terrible about forgetting their exact location and digging into them. They seem to like dryer conditions, especially when dormant, so I wouldn't recommend additional water.