How long is a miniature? A miniature is a short game of chess. Depending on the forums you ask in or the blogs you look at, the length of the miniature is always a problem.

Is there a standard number of moves under which the game is considered to be a miniature? Is there a reason that number is special?

Not even Wikipedia has a concrete definition regarding this aspect of the game.
I have an old book in my house, 500 King's Gambit Miniatures, and in the first pages the games, at the least, didn't pass 30 moves. I think it is a very good definition.