This seems to be a question that many have asked and while I can't give you anything concrete here is what Larry Mayer on the official site has to say:
Just like a change-up in baseball, the Bears used the no-huddle offense to catch the Giants off guard on their first possession of the game. If you throw a change-up on every pitch, it won't be long before the other team starts depositing the ball over the fence. The Bears went into Sunday's game with a menu of 12-14 plays in their no-huddle offense, and had they stuck with it the entire game, it wouldn't have taken the Giants long to figure out when the Bears were going to run and when they were going to pass. In addition, the offense gets just as tired as the defense in those no-huddle situations. Unlike a team like the Indianapolis Colts that runs the no-huddle constantly, it would have been a dramatic change for the Bears to do something like that. I think it would have made the offense--which committed no turnovers in the game--much more prone to making mistakes. The Bears didn't lose to the Giants because they abandoned the no-huddle offense. They lost because their defense gave up two late touchdowns and their offense was forced to settle for field goals after picking up first downs at the Giants' 5-, 14- and 13-yard lines.