When Shehechiyanu is said "publicly" (i.e., on holidays, Kiddush or prior to certain mitzvoth - occasions when everyone must say it vs. say when wearing new clothes.) it is generally done just once on the occasion of the first time performing the mitzvah.
However, I am a bit puzzled regarding understanding this rule of "first time only" esp. when it concerns Yom Tov Sheini in Galut.
There seems to be an inconsistency, regarding things done during Succot as well as Rosh Hashanna.
On Rosh Hashanna, the mitzvah to blow the shofar is one day. By that logic, we should be saying Shehechiyanu only on the 1st time we blow the shofar. Yet, we say Shehechiyanu on the 2nd day, also. I understand that the reason we do it on the 2nd day is due to sfeika deyoma (we're not sure which day is the 1st day.)
In contrast, the mitzvah for taking Lulav (from the Torah's statement) is on the first day, only. Outside of Israel, we say Shehechiyanu on the 1st day, only, not on the 2nd day. Why isn't this following the same rules as for shofar? If we're not sure which day was the first day, why shouldn't we say Shehechiyanu on lulav on the 2nd day?