Language agents read code, tool output, and dialogue in contexts that grow at every step. Dynamic sparse attention lets a small indexer choose the earlier tokens each query attends to, but the indexer still scores the whole prefix at every layer. Cross-layer reuse methods such as IndexCache rerun the indexer at only some layers, with one fixed pattern for every input. In an agent, the relevant evidence can change abruptly when a traceback or test result arrives, so fresh selections matter more at some steps than at others. We propose Adaptive Index Reuse (AIR), which keeps IndexCache's execution and learns, for each segment of an agent episode, how many layers refresh their selection. A small controller reads signals from completed computation and the latest tool event, chooses a pattern from a nested library, and learns from terminal task reward under an expected compute budget. On Qwen3-4B-Instruct-2507 with a 128K context, AIR improves success over the strongest static schedule at matched cost on SWE-bench Verified (27.0% to 32.4%), Terminal-Bench 2.0, and three $τ^2$-bench domains, and it lowers time per successful task on all five. Across 50 backbone, context, and benchmark settings, it matches or exceeds that schedule in 44.

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