Hospital logistics management faces growing pressure from internal operations and external emergencies, with artificial intelligence (AI) holding untapped potential to boost its resilience. This study explores AI's role in enhancing logistics resilience via a mixed-methods case study of H Hospital, combining 12 key informant interviews and a full survey of 151 logistics staff, with the PDCA cycle as the analytical framework. Thematic and quantitative analyses (hierarchical regression, structural equation modeling) were adopted for data analysis. Results showed 94.7% staff perceived AI application, with the strongest improvements in equipment maintenance (41.1%) and resource allocation (33.1%), but limited effects in emergency response (18.54%) and risk management (15.23%). AI integration positively correlated with logistics resilience (\b{eta}=0.642, p<0.001), with management system adaptability as a positive moderator (\b{eta}=0.208, p<0.01). The PDCA cycle fully mediated the AI-resilience relationship. We conclude AI effectively enhances logistics resilience, dependent on adaptive management systems and structured continuous improvement mechanisms. Targeted strategies are proposed to form an AI-driven closed-loop resilience mechanism, offering empirical guidance for AI-hospital logistics integration and resilient health system construction.