Robin, thanks for the links. They were very helpful. As you and Daphne pointed out, I think it's likely that they're overcrowded. In one of the articles your links took me to, the author said this is a good time of year to divide and re-pot the rhizomes, so I think I'll get a large pot and combine the plants in my three small pots in it.
I was totally surprised by their watering needs. Summers here have temps always in the high 90's and often over 100 deg. I'm used to watering every morning. Letting the irises go a week or two before a deep watering just seems wrong to me. I may have to research that some more!