ACC seems to be hyper-attentive to brake lights ahead, so if the person ahead of you braked, that may have triggered your ACC to stop the car. But it sounds like a problem with your car, since it has happened several times.
You are probably aware that you cannot "set" the ACC unless you are going over about 10 mph.
You are probably aware that you cannot "set" the ACC unless you are going over about 10 mph.