I've been growing day lilies for about 35 years. Bloom is very variable on the plants. Some bloom freely over a short period, others bloom over a longer period, some bloom early, others midseason, and still others late. One thing has surprised me this year. I have plants that have always bloomed relatively early with a one time bloom period. Those plants were moved to the vegetable garden where they get more water and more fertilizer. This year some of them were still blooming as of yesterday. And those plants have been blooming since May or June. Have never had that happen before. There are less flowers than at peak, but still one, two or three blooms per day. Think that they are about finished now however.
So from this year's experience I would say, try different varieties, try planting them in various locations, and give them a little fertilizer or compost and water regularly during drought. You will likely extend the bloom season quite a bit. Finally, any perenial that has the seeds removed, is quite likely to be forced into a secondary bloom. I don't see why that would be different for daylilies, though for me the results of the practice have been marginal.