AI agents are increasingly used in long, multi-turn workflows in both research and enterprise settings. As interactions grow, agent behavior often degrades due to loss of constraint focus, error accumulation, and memory-induced drift. This problem is especially visible in real-world deployments where context evolves, distractions are introduced, and decisions must remain consistent over time. A common practice is to equip agents with persistent memory through transcript replay or retrieval-based mechanisms. While convenient, these approaches introduce unbounded context growth and are vulnerable to noisy recall and memory poisoning, leading to unstable behavior and increased drift. In this work, we introduce the Agent Cognitive Compressor (ACC), a bio-inspired memory controller that replaces transcript replay with a bounded internal state updated online at each turn. ACC separates artifact recall from state commitment, enabling stable conditioning while preventing unverified content from becoming persistent memory. We evaluate ACC using an agent-judge-driven live evaluation framework that measures both task outcomes and memory-driven anomalies across extended interactions. Across scenarios spanning IT operations, cybersecurity response, and healthcare workflows, ACC consistently maintains bounded memory and exhibits more stable multi-turn behavior, with significantly lower hallucination and drift than transcript replay and retrieval-based agents. These results show that cognitive compression provides a practical and effective foundation for reliable memory control in long-horizon AI agents.