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The token-level extractive compressors widely used for general LM context are structurally inappropriate for LLM agents: across 17 (env, backbone, method) cells spanning two independent token-level method families, every cell collapses to mean reward <= 0.05 despite 1.3-13.3x realized compression. We name and characterize this failure mode as action-grammar destruction -- the tokens carrying action semantics (identifiers, brackets, action verbs) are exactly those self-information ranks lowest, so a general-purpose compressor reliably removes them and the environment rejects the residual. The diagnosis points to step-granularity compression. We introduce AGORA, an inference-free step-level compressor combining a structural prompt parser, an always-keep floor for format- and recency-critical content, and a 125M-parameter relevance scorer trained on counterfactual next-action-change labels (~2ms/step, zero per-step LLM toll). Across the compared inference-free and LLM-based methods, AGORA is the only one retaining >= 75% uncompressed performance in 8 of 9 cells (with the lone exception at 73%); a four-way component ablation isolates the structural floor as the dominant quality lever and the learned scorer as the source of 1.0-11.5x adaptive end-to-end compression from a single fixed keep ratio.