The correct answer is C) remaining open until a preset pressure drop occurs. A boiler safety valve must be capable of remaining open until a preset pressure drop occurs. This is because the safety valve is designed to prevent the boiler from exceeding its maximum safe working pressure. Once the pressure in the boiler reaches the preset valve, the safety valve must open to release the excess pressure and prevent a dangerous overpressure situation. The valve must remain open until the pressure drops to a safe level, at which point the valve can close again. The other answer choices are incorrect because they do not accurately describe the required function of a boiler safety valve. The valve should not close with a chattering motion, remain open indefinitely, or open gradually, as these would not effectively relieve excess pressure in the boiler.