Large language models (LLMs) are increasingly used for medical consultation and health information support, where safety depends not only on medical knowledge but also on robust responses to unclear, inconsistent, or misleading patient input. However, most existing medical LLM evaluations assume idealized and well-posed patient questions, limiting their realism. We study challenging patient behaviors that commonly arise in real medical consultations and complicate safe clinical reasoning. We define four clinically grounded categories of such behaviors: information contradiction, factual inaccuracy, self-diagnosis, and care resistance. For each behavior, we specify concrete failure criteria that capture unsafe responses. Building on four existing medical dialogue datasets, we introduce CPB-Bench (Challenging Patient Behaviors Benchmark), a bilingual (English and Chinese) benchmark of multi-turn dialogues annotated for these behaviors. We find that although models perform well overall, they exhibit consistent behavior-specific failures, especially when handling contradictory or medically implausible patient information. We further evaluate four intervention strategies and find inconsistent improvements, with some interventions introducing unnecessary corrections. We release the dataset and code.