Though promising in healthcare consultation applications, large language models (LLMs) face critical limitations in retaining and utilizing long-term memory across multi-turn interactions. In particular, existing memory enhancing paradigms are constrained by limited context windows and embedding-based retrieval, often failing to maintain task relevance and still suffering from memory prototype collapse in multi-turn healthcare consultation. To address these challenges, we propose a cognitively-inspired memory framework named MemoryART, which is grounded in Adaptive Resonance Theory (ART)—a cognitive and learning theory of how humans and animals adapt to dynamic environments. MemoryART employs three memory modules—working memory, episodic memory, and semantic memory to support task-aware memory organization and dynamic retrieval. Specifically, episodic memory provides the storage of specific experiences along with contextual clues, which is crucial for managing patient-specific information and perfect for multi-turn healthcare consultation interactions. Building upon this concept, MemoryART leverages multi-channel competitive learning and resonance matching to enable efficient and interpretable episodic memory encoding, alleviating issues of prototype collapse and noisy memory associations. For evaluation, we construct a long-term medical dialogue benchmark called MediLongChat using a LLM-based generation pipeline. The resulting dataset features realistic, multi-disease chat histories, each exceeding 100K tokens across 20–30 dialogues, simulating real-world healthcare interaction patterns. Our experimental results show that MemoryART outperforms mainstream approaches in memory-intensive tasks, achieving SOTA results and significantly reducing token consumption across five popular LLMs, confirming its effectiveness and efficiency in providing scalable, reliable memory for LLMs in healthcare. Code and datasets are available at \url{https://github.com/dairkkriad/MemoryART}