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Large Language Models (LLMs) have emerged as powerful operators for evolutionary search, yet the design of efficient search scaffolds remains ad hoc. While promising, current LLM-in-the-loop systems lack a systematic approach to managing the evolutionary process. We identify three distinct failure modes: Context Pollution, where experiment history biases future candidate generation; Mode Collapse, where agents stagnate in local minima due to poor exploration-exploitation balance; and Weak Collaboration, where rigid crossover strategies fail to leverage parallel search trajectories effectively. We introduce Progress-Aware Consistent Evolution (PACEvolve), a framework designed to robustly govern the agent's context and search dynamics, to address these challenges. PACEvolve combines hierarchical context management (HCM) with pruning to address context pollution; momentum-based backtracking (MBB) to escape local minima; and a self-adaptive sampling policy that unifies backtracking and crossover for dynamic search coordination (CE), allowing agents to balance internal refinement with cross-trajectory collaboration. We demonstrate that PACEvolve provides a systematic path to consistent, long-horizon self-improvement, achieving state-of-the-art results on LLM-SR and KernelBench, while discovering solutions surpassing the record on Modded NanoGPT.