Pests which will sometime infect daylilies include aphids, spider mites, thrips, slugs and snails. If you find that you need to spray your daylilies you should use something that has been rated for use on daylilies or you know for sure will not harm the plants. He didn't kill his daylilies, but that year he didn't have very many blooms. I use a stronger solution than is recommended and use repeated applications over several months. If the insecticide passes this test, then I feel comfortable using it on the rest of my plants.
Daylilies are a relatively disease free plant.
Crown rot is the only daylily disease that I have had to deal with here in the Salt Lake area. This disease is limited primarily to the deep south and usually only affects a small number of my plants. However, it can kill a daylily in a matter of only a few days. Daylilies multiply by sending up new fans right next to the old fans. Dig up the entire clump and shake off the dirt.