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Large Language Models (LLMs) deployed in multi-turn conversational settings are typically served under a naive full-history pattern: the entire prior transcript is re-submitted as input context at every turn. This has two known consequences, usually studied separately: growing computational and billed cost, driven by the quadratic cost of self-attention over a linearly growing context, and degrading answer quality at long context lengths, documented in the “lost-in-the-middle” and “context rot” literature. We implement and empirically evaluate Adaptive Context Pruning (ACP), a contextmanagement strategy combining a sliding window, TF-IDF relevance-budgeted retention of older turns, and periodic extractive summarization, against naive full-history retention, on a controlled synthetic multi-turn benchmark with probe questions requiring recall of specific facts planted earlier in the conversation. Using a real LLM (Groq-hosted Llama-3.1-8B-Instruct) to answer all probes and grading answers against ground truth, we find that at a conversation length of 183 turns, naive retention consumes approximately 14.9× more context tokens than ACP, and its real measured API cost grows correspondingly; more importantly, naive retention’s probe accuracy collapses under this setup, from 100% up to 78 turns to 0% at 183 turns, where all of its requests are rejected outright by the provider for exceeding a free-tier tokens-per-minute limit for this model (verified in §6.4 to be a tier-specific rate limit, not the model’s much larger advertised context window), whereas ACP sustains 100% probe accuracy at every conversation length we tested (up to 183 turns), using a bounded context of under 700 tokens throughout, with sub-millisecond-to-low-single-digit-millisecond own bookkeeping overhead per turn. We report these results with full transparency about the experiment’s scope: a synthetic dataset, TF-IDF rather than neural embeddings for relevance scoring, extractive rather than LLM-based summarization, and a single small open-weight model behind a single inference provider. We present a theoretical cost model motivating why this failure mode is expected under naive retention, and discuss what would be required to validate these findings at larger scale and with production-grade components.