Pam, salt doesn't hurt daylilies. I live a block from the beach and a block from the intercoastal. Even cars inside the garage get a coating of salt! Daylilies don't care!
My best guess?
(1) If they are planted near queen palms, palm roots will come to the surface to feed off any fertilizer used on the daylilies.
(2) If they are grown in the sand, no amount of fertilizer will work to make them thrive. That's why I grow in raised boxes.
(3) I agree with Betty, it sounds like those plants may have dormancy in them. Dormants will not live on the barrier island in Daytona nor will they live further south. They may not be classified as dormants--they may be classified as semi-evergreens. Even SEV's have too much dormancy for me--that's why I concentrate on researching parentage. If parent plants aren't provided (Salters usually don't) then you have no information to make a good decision.
Take your pick. I've got through it all and now have lovely plants. You might pot up those daylilies and let them live in pots. That usually works unless they have dormancy!