Will there be a Yom Tov Sheni after Moshiach comes?
After moshiach comes, all Jews will live in Eretz Yisrael, either in its original form, or in a different form described by Yechezkel toward the end of his prophesies. Either way, there will be no need for yom tov sheni. Even if, during yemos hamashiach, one were to be in Chutz La'aretz, I doubt they would need to observe yom tov sheni, as they would be considered residents of Eretz Yisrael, who always observe one day regardless of their temporary location.
EDIT: It is true, as SimchasTorah suggests in the comments, that the Chasam Sofer, who in general took a more mystical, less technical approach to yom tov sheni, believes that after Mashiach comes, we will celebrate yom tov sheni to remind us of the long galus we were in previously. It can be found here: http://www.hebrewbooks.org/pdfpager.aspx?req=21254&st=&pgnum=131&hilite= (paragraph starting "l'maan")
The Lubavitcher Rebbe says that it is possible that Yom Tov Sheni will continue to be celebrated because it has been done for so many generations. Even though the calendar will be replaced with the Sanhedrin declaring the month based on testimoney, it will still not be technically necessary to keep two days anywhere, as everyone will know right away when the new month started.
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