Automatic prompt optimization (APO) uses algorithms to automatically refine prompts for LLMs, effectively reducing human effort in prompt engineering. However, applying APO to memory-enhanced conversational agents presents unique challenges. These agents leverage memory to retain information from historical interactions with users and provide context-aware and personalized responses. Optimizing prompts for these agents is challenging due to their complex, interconnected modules that include memory writing, reading, and response generation. This paper introduces a data-efficient framework for APO in these agents. Our approach leverages LLMs to holistically optimize the prompts of all agents. We also introduce an automated evaluation module that not only provides a holistic quality score for responses but also performs error attribution, pinpointing failures within the specific modules. More importantly, to ensure the evaluation module aligns with human judgment, we develop a data-efficient active sampling algorithm with convex optimization to select the most informative samples for human feedback and prompt improvement. We conducted experiments on two health-related conversation datasets to demonstrate the effectiveness of the proposed framework.