admmad said:
Although I do not know of an insect that damages daylily seed pods specifically in that manner, there might be insects that suck juices from plant tissues (like aphids) but that use firmer tissues, like scapes or seed pods. Sue @Sooby may have a much better idea of what might cause appropriate damage that could lead to rotting.
I would suspect some kind of "true bug", there are several that are potential pests of daylilies. At least some can inject what is sometimes referred to as a "toxin" although I think I recall that it may be some kind of growth regulator. The tarnished plant bug (Lygus lineolaris) is one that comes to mind In that category although we don't know exactly what damage it does to daylilies - it tends to go for reproductive parts of plants. I once found a TPB nymph on some damaged and rotting daylily stamens. Another might, and I stress might, be a milkweed bug because it is a seed feeder and has been noted on daylilies although could just be hanging out. You may have difficulty noticing "true bugs" because they are much more mobile than something that stays in place feeding for long periods like an aphid. Adult bugs will often duck under a leaf or bud when you approach, and the young nymphs are tiny and far more agile than an aphid. If you have any cool mornings there, have a look for something like that. They tend to be more sluggish when it's cool. Get a picture to post if you see a possible suspect.