Large Language Model (LLM) agents struggle with ultra-long-horizon tasks requiring hundreds or thousands of interaction steps. Traditional context management approaches face a fundamental dilemma: preserving complete histories rapidly exhausts context windows and forces crude truncation, while aggressive summarization discards critical information prematurely. We propose Predictive Adaptive Context Extraction (PACE), a novel framework that reconceptualizes context management as a Next Step Prediction problem. Inspired by neural attention, PACE dynamically constructs context by adjusting historical memory granularity based on its predicted relevance for the next action. Comprehensive evaluation across diverse benchmarks and models demonstrates that PACE consistently improves task success rates, with larger gains on complex tasks and robust cross-lingual performance. Crucially, PACE enables agents to sustain effective reasoning for 4,897 interaction steps in ultra-long-horizon scenarios, achieving a 66.2 improvement over the full-context ReAct baseline and 5.1 over advanced folding baselines. This fundamentally advances the capability of LLM-based agents in previously intractable long-horizon scenarios. Our code and data are available at https://anonymous.4open.science/r/PACE-B000/.