Across independent sessions, dialogue systems built on large language models do not retain prior context unless an external memory layer organizes and retrieves it. Most memory sys- tems treat this as a retrieval problem, assuming that surfacing the right past content is the pri- mary lever for accuracy. We report evidence that this view is incomplete: holding retrieval fixed, how retrieved context is organized and presented to the model is an independent and substantial driver of answer accuracy. We demonstrate this with the Context Persistence Protocol (CPP), a modular memory layer that groups dialogue into topically coherent seg- ments, retrieves them with hybrid lexical and semantic search, and highlights the single most informative sentence in each segment before generation. Across two long-term memory benchmarks, CPP attains session-level retrieval scores that are identical to those of an un- bounded flat-retrieval baseline on LoCoMo and slightly lower on LongMemEval, yet it answers substantially more questions correctly, with the largest gains on multi-hop reasoning. These results suggest that the organization and presentation of retrieved context, rather than retrieval coverage alone, is a major driver of the difference.