Yeah that decision was made by the competition committee back when Reliant Stadium was built.
League decides 30 mins or so before kickoff whether the roof is closed...depending on whether. If it's a hailstorm going on, then I think we know the decision.
If the roof is closed at the beginning of the game, it's to stay close throughout the course of the game. Same as if the roof is open at the beginning of the game, it has to stay open even if the whether changes.