StableMind addresses the problem of long-term personality drift in large language model (LLM) agents, where short-term coherence does not guarantee stable behavioral traits across extended interactions. We identify this as a stability–plasticity trade-off: systems must remain adaptable to new observations while preserving a consistent underlying personality structure. We propose StableMind, a memory- and reflection-based architecture that separates short-term belief updates from long-term trait evolution. Incoming interactions are encoded as structured perceptions and incrementally integrated into entity-specific beliefs. A reflection mechanism periodically evaluates belief drift against established baselines, triggering trait updates only when predefined thresholds of magnitude, confidence, and observation frequency are satisfied. This design introduces discrete adaptation cycles that stabilize identity formation while preventing abrupt personality shifts. Experimental analysis shows improved consistency in agent behavior over long interaction sequences compared to baseline approaches.