There are some reasons listed in the FAQ at the top of the page.

One reason not mentioned is some cultivars are not as vigorous as others. Be sure you are not using a high nitrogen (ie. 10-5-5) fertilizer.

Do they have enough sun? First year they probably had buds from before they got to you. Second year may not have enough sun to produce another bud.
Laetitia

The iris from the West Coast often take several years to adapt to the different climates and rebloom. I'll get about 75% first year bloom from new ones and then most don't bloom again for two or more years, by which time down here in TN the rhizomes have shrunk and gotten very tough to withstand the heat and dry summers. Then they bloom every year.

I had Dynamite iris on the east side of the house (shade after 1pm) and it has never bloomed in 4 years. Other irises in the same bed bloomed during that period at least once. I was told to move it to another spot, that sometimes even 6 feet away from the previous spot could make a picky iris bloom.