Krodri, is this your first experience with daylilys? I may be interpreting your 1st post incorrectly but when I read it, it sounded like what you are calling the stem is in actuality the scape stem ~~~ that would be the portion of the plant that has the buds & blooms on it. Otherwise, daylilys don't have "stems", only leaves. You said the "grass part" is still green. The grass part is the leaves & they don't have "stems". Daylilys don't bloom forever, they send up a scape (stem) which has buds on it that turn into blooms. Each bloom only lasts one day & then it dies. When all the buds on that "stem" have bloomed, then the "stem" turns brown & dies. That stem will never have anymore blooms on it again. A new "stem" or scape can come up with buds on it but the original scape stem will die. I'm wondering if you knew this. It sounded to me like you thought that "stem" (scape) was supposed to produce more & more buds that would turn into blooms.
Please forgive me if I misread your original post. But if what I laid out above is in fact what happened, then do not worry. The daylily is just doing what it is supposed to do & everything is fine. As the others have said, we cut the stems after all the buds have opened b/c the stem is no longer needed & cutting it conserves energy for the leaves/roots. Depending on the variety of daylily you have, they will have a bloom period & that may be early, mid season or late season but rarely do daylilys bloom year round. In other words, one plant really doesn't bloom from say March through November.