Large Language Models (LLMs) are increasingly expected to interact with users over long time horizons. However, due to their finite context window, LLMs cannot retain all past interactions, making long-term memory management essential for storing, updating, and retrieving historical information beyond the context limit. Although recent memory systems attempt to address this issue by storing historical information externally, existing approaches suffer from three key limitations: flat text-based memory organizations fail to capture explicit relations among memories, structured memory systems often destructively overwrite evolving facts, and current retrieval mechanisms remain query-agnostic and passive when evidence is incomplete. REAL constructs long-term conversational memory as a temporal and confidence-aware directed property graph, where each atomic fact is represented with entities, relations, valid-time intervals, confidence scores, and exploration intent labels. During memory construction, REAL adopts a non-destructive temporal update strategy that preserves parallel fact versions and their validity intervals, enabling faithful tracking of fact evolution. During retrieval, REAL anchors query-relevant root entities, decouples their exploration intents, and performs semantic evaluator-guided hybrid beam search to extract compact memory subgraphs. It further incorporates counterfactual inference to repair unreliable retrieval states and recover missing memory evidence through implicit logical relations. Comprehensive experiments demonstrate that REAL substantially improves long-term memory performance over flat-text, graph-based, and existing memory baselines, achieving an average improvement of 22.72\%.