1. To my mind, it's easy enough to make the dragons themselves "holy" figures in the minds of their respective people. The fact that one is good and one is evil and both are godlike in the minds of their followers should give them enough philosophical impetus to fight.
2. Maybe the "reds" don't know one of the silvers is out of commission yet. The threat of full scale war might be enough of a deterrent at the moment. The thrust of the plot could revolve around keeping these sorts of things secret until the silver is healed or some other assistance can be gained or preparations can be made.
3. Perhaps this closely guarded secret is kept by the high priest of the "silvers," who has to keep up appearances and is slowly losing ground/losing control.