We present R-Debater, an agentic framework for generating multi-turn debates built on argumentative memory. Grounded in rhetoric and memory studies, the system views debate as a process of recalling and adapting prior arguments to maintain stance consistency, respond to opponents, and support claims with evidence. Specifically, R-Debater integrates a debate knowledge base for retrieving case-like evidence and prior debate moves with a role-based agent that composes coherent utterances across turns. We evaluate on standardized ORCHID debates, constructing a 1,000-item retrieval corpus and a held-out set of 32 debates across seven domains. Two tasks are evaluated: next-utterance generation, assessed by InspireScore (subjective, logical, and factual), and adversarial multi-turn simulations, judged by Debatrix (argument, source, language, and overall). Compared with strong LLM baselines, R-Debater achieves higher single-turn and multi-turn scores. Human evaluation with 20 experienced debaters further confirms its consistency and evidence use, showing that combining retrieval grounding with structured planning yields more faithful, stance-aligned, and coherent debates across turns.