A. We have two days of every yom-tov because of the calendrical doubt (s’feka d’yoma) as to which is really the correct day. As either day could be correct, we say Shehecheyanu when we recite Kiddush on both the first and the second days of a yom-tov.
However, ancient tradition and usage regards Rosh HaShanah as one long day, yoma arichta. What appear to be the two days of Rosh HaShanah apply everywhere, even in Israel, and two days were even observed in the Temple. Nonetheless, Shehecheyanu is recited on both days as on any yom-tov (Aruch HaShulchan, Or. Ch. 600:4).
Why then do we not recite the blessing on both days of Sukkot when talking the lulav? Perhaps the lulav is a special case, since the Torah says, “On the first day…” (Lev. 23:40).