The Additional Day of Yom-Tov in the Diaspora 
After the future Redemption, when the advent of the New Moon and
the proclamation of Rosh Chodesh will once again be determined by
the testimony of eye-witnesses,  there will no longer be any
doubt as to which day was sanctified as such  because it will
then be possible to inform all Jews of this instantly.
Despite all this, it could be argued that even then we will
continue to celebrate the Diaspora's Additional Day of Yom-Tov -
simply because Jews have been accustomed to doing so for so many
For a parallel, note the case of Shavuos.
Here there is no calendric doubt, since its timing hinges
not on a particular date in the month of Sivan, but on the
counting of fifty days from the fifteenth of the earlier month
of Nissan. 
By then, the emissaries from the Beis HaMikdash in Jerusalem were
surely able to reach any outlying community and to inform them
which day had been sanctified as Rosh Chodesh Nissan (and
consequently which day was the fifteenth of Nissan).
Nevertheless, even though Shavuos thus involves no calendric
doubt, its Additional Day is celebrated as Yom-Tov - simply in
order not to discriminate between the Three Pilgrim Festivals,
 by downgrading it from their accustomed status.
From a talk of the Rebbe Shlita on the
afternoon of Simchas Torah 5749 
- (Back to text) In the original, al pi hare'iyah; i.e., as formerly, in
Temple times (Rosh HaShanah 1:3; Rambam, Hilchos Kiddush
- (Back to text) Vayikra 23:15-21; Devarim 16:9-10.
- (Back to text) Rambam, Hilchos Kiddush HaChodesh 3:12.
- (Back to text) Siddur Tehillat HaShem, p. 341.
- (Back to text) In the Aram. original, deoraysa.