This paper highlights that the low adoption of closed-loop insulin delivery systems (CLIDS) in patients with type 1 diabetes is due to behavioral, psychosocial, and social barriers, rather than technical issues. We propose ChatCLIDS, a new benchmark to address this issue. ChatCLIDS simulates interactions with a nurse agent using a variety of persuasive strategies, utilizing expert-validated virtual patients. This allows for multidimensional assessments, considering prolonged consultations and social pressure situations. Our findings demonstrate that large-scale language models (LLMs) adapt their strategies over time but struggle to overcome resistance, particularly under realistic social pressures. This highlights the current limitations of LLMs in behavioral change and provides a high-fidelity, scalable testbed for the development of reliable persuasive AI in healthcare and beyond.