Production AI agents frequently receive user-specific queries that are highly repetitive, with up to 47\% being semantically similar to prior interactions, yet each query is typically processed with the same computational cost. We argue that this redundancy can be exploited through conversational memory, transforming repetition from a cost burden into an efficiency advantage. We propose a memory-augmented inference framework in which a lightweight 8B-parameter model leverages retrieved conversational context to answer all queries via a low-cost inference path. Without any additional training or labeled data, this approach achieves 30.5\% F1, recovering 69\% of the performance of a full-context 235B model while reducing effective cost by 96\%. Notably, a 235B model without memory (13.7\% F1) underperforms even the standalone 8B model (15.4\% F1), indicating that for user-specific queries, access to relevant knowledge outweighs model scale. We further analyze the role of routing and confidence. At practical confidence thresholds, routing alone already directs 96\% of queries to the small model, but yields poor accuracy (13.0\% F1) due to confident hallucinations. Memory does not substantially alter routing decisions; instead, it improves correctness by grounding responses in retrieved user-specific information. As conversational memory accumulates over time, coverage of recurring topics increases, further narrowing the performance gap. We evaluate on 152 LoCoMo questions (Qwen3-8B/235B) and 500 LongMemEval questions. Incorporating hybrid retrieval (BM25 + cosine similarity) improves performance by an additional +7.7 F1, demonstrating that retrieval quality directly enhances end-to-end system performance. Overall, our results highlight that memory, rather than model size, is the primary driver of accuracy and efficiency in persistent AI agents.