On a leap year, when a second Adar is added, we celebrate Purim on the second Adar. I would think it should be celebrated on the first Adar, since the Megillah goes out of its way in several places to identify Adar as the "twelfth month." Adar Sheni would seem to be the thirteenth month counting from Nisan.
So what is the reason that Purim was instituted to be observed on Adar Sheni during a leap year?