We present NeuSymMS, an adaptive memory system that enables large language model (LLM) agents to learn, remember, and reason about users across sessions via a hybrid neuro-symbolic architecture. NeuSymMS couples neural fact extraction from unstructured dialogue using LLMs and a CLIPS-based expert system that classifies, deduplicates, and reconciles facts under explicit lifecycle rules. The system represents knowledge as subject-relation-value triples stored in relational database management system. It supports user/agents/agent-to-agent scoping, and implements a dual-horizon (short-term and long-term) memory model. IT leverages access-based promotion and time-based pruning of the memory on both horizpons. NeuSymMS maintains continuity of memory while avoiding context-window bloat and cross-entity contamination. We argue that this architecture offers a practical path to trustworthy, auditable memory for production agentic systems and discuss its novelty relative to log retrieval, summarization, and key-value approaches.