Deck Devastation Virus (DDV) destroys all monsters with 1500 or less ATK on your opponent's field and in the hand at the time it resolves. After that, it will destroy all monsters with 1500 or less ATK that your opponent draws (and you get to check each of his/her draws) until the end of your opponent's 3rd turn.
Destroying monsters on the field and in the hand only occurs 1 time, when the card initially resolves. After that, it will only destroys monsters that are drawn. If your opponent summons a monsters with 1500 or less ATK it won't be destroyed, and the same goes for if they move a monster with 1500 or less ATK to their hand by a method other than drawing it.