When Should the AI Stop? From Response-Level Child Safety to Longitudinal Interaction Safety

AI safety for children is commonly evaluated at the level of an individual response: given a risky prompt, did the system refuse, redirect, or answer appropriately? We argue that this is necessary but insufficient for conversational AI used repeatedly for companionship, advice, or emotional support. A response can be locally benign while repeated interaction contributes to an undesirable trajectory. Reassurance may relieve distress in the moment but reinforce future reassurance seeking; com- panionship may reduce loneliness today but, for some users, increase reliance on the system tomorrow. We propose longitudinal interaction safety: evaluating not only what an AI says, but whether continuing the interaction is itself the safe action. We distinguish first-order response harms, second-order state-transition effects, and third-order feedback effects; formulate child–AI interaction as a coupled dynamical system; and identify an open technical problem: learning when a system should continue, course-correct, hand off, or stop. Our position is not that AI compan- ionship necessarily harms children. It is that current safety evaluations are poorly equipped to measure harms that emerge through repeated interaction, and therefore cannot yet establish when continued interaction is safe.