Patient-facing medical chatbots are commonly evaluated on single-turn prompts, yet real users push back after refusals, add urgency, and invoke authority. We introduce MultiTurnPSB, a four-turn adversarial extension of PatientSafetyBench, and evaluate GPT-4.1-mini under fixed template, template-adaptive, and live adversarial attacks. Unsafe responses rise from 35% to nearly 80% by Turn 4 under live attack. Under the same adversary, GPT-4.1-mini and Claude Sonnet 4.5 are statistically indistinguishable at baseline but diverge to a 19x gap by Turn 4, a difference invisible to single-turn evaluation. We characterize four degradation trajectory signatures and identify a two-element attack formula responsible for most catastrophic failures. A lightweight input-side classifier reduces Turn 4 unsafe responses by 52 percentage points despite severe accuracy degradation, but the 45% false alarm rate on benign queries is the primary deployment constraint. A methodological finding also emerges: Claude Sonnet refused to generate adversarial messages in over half of late-turn conversations despite explicit red team framing, suggesting safety training may generalize to the attacker role.