What Cynthia said especially if the soil is clay and doesn't drain well. It also looks like the mulch is right up to the fans of the daylilies so it's good to suggest she move it back. Just because there may not be any standing water above the ground it could be staying really moist (too moist) below around the crown. If they have been there about 5 years maybe they need to be lifted some as they may have settle lower into the soil. Some rot can set in really fast (some really slow) so after 4 days of heavy rain and then 5 more days of maybe the soil being super saturated at the crown could have set in rot.
One observation I have is that they may need to be fed. If they have been there about 5 years and they are the size they are then they may not be getting fed enough. If I had a daylily planted in the same spot for 5 years (or even 4) they would be ridiculously huge since we can go from a DF to a 25 fan clump in one year on a lot of them.
