Why are there certain days such as Pesach Sheni where we do not say Tachanun at Shacharit but we do say it at Mincha before that day? What other days does this occur?

There are three days that by the Ashkenazi custom one does not say Tachanun on them but says on the Mincha before. These are Pesach Sheni, Erev Rosh Hashana and Erev Yom Kipur. The reason is that these days merit because of others: Erev Rosh Hashana because of Rosh Hashana... and Pesach Sheni because of the Pesach. Therefore, the day before them does not once again merit. Rabbi Ro'i Margalit