Life is too short and garden resources (space, water, food, light, the gardener's time and energy) too precious to waste on a daylily which does not thrill you, or which can be replaced by something better. (YOU decide what is "better" for your garden, not someone else. Newer does NOT necessarily equal better.)
Exceptions may sometimes be made in the case where/if you are hybridizing, and the daylily has certain genes which you absolutely must have (and which are hard to come by). In that case, you keep the sketchy plant as long as needed (i.e until and if you get better offspring from it, or give up trying), and then you punt it. In a purely ornamental garden, though, daylilies must earn their keep.
"Am I eager to see this daylily begin bloom each year?" and "Am I sad to see the last flower open on this daylily?"
"Yes" = keep it ("No" should make yourself ask why not...)
"Would I miss it if it was gone from the garden?"
"Yes" = keep it ("No" should make you ask yourself why you are keeping it...)
"Is it an ornament to the garden?" "Yes" = keep it
("No" and "I don't know" in this case may require some discernment, as sometimes plants don't perform their best where they are first placed in the garden. If the daylily in its 2nd year of bloom is (still) visual trash, that should immediately result in a trip to the compost pile or yard waste bin; odds are that it is not going to get any better so don't waste any more time or space on it. (Exceptions may or may not be made for seedlings, which may be punted their first year of bloom. Seeding bed space is in short supply, so you can only keep so many seedlings around for a second look.) If the daylily in question is not obviously trash, but it doesn't look quite right where it is, and/or is not meeting its registered specs, then maybe you should try it in a different spot in the garden, or plant it in the ground (if it is in a pot). Such changes of venue can sometimes work wonders. (And sometimes not... If, for example, the daylily needs warm nights to open fully, and you don't have warm nights, well....))
I'm sure you can think of more questions to ask yourself. (Right now, I am asking myself these very same questions, on daylilies both new and old.)
Fwiw, if that daylily were in my garden, and this was its second year of bloom and it looked like that, it would be going into the yard waste bin. I wouldn't inflict that plant on anyone else.
JMHO and YMMV.
