Time toxicity, the cumulative healthcare contact days from clinical trial participation, is an important but labor-intensive metric to extract from protocol documents. We developed TimeTox, an LLM-based pipeline for automated extraction of time toxicity from Schedule of Assessments tables. TimeTox uses Google's Gemini models in three stages: summary extraction from full-length protocol PDFs, time toxicity quantification at six cumulative timepoints for each treatment arm, and multi-run consensus via position-based arm matching. We validated against 20 synthetic schedules (240 comparisons) and assessed reproducibility on 644 real-world oncology protocols. Two architectures were compared: single-pass (vanilla) and two-stage (structure-then-count). The two-stage pipeline achieved 100% clinically acceptable accuracy ($\pm$3 days) on synthetic data (MAE 0.81 days) versus 41.5% for vanilla (MAE 9.0 days). However, on real-world protocols, the vanilla pipeline showed superior reproducibility: 95.3% clinically acceptable accuracy (IQR $\leq$ 3 days) across 3 runs on 644 protocols, with 82.0% perfect stability (IQR = 0). The production pipeline extracted time toxicity for 1,288 treatment arms across multiple disease sites. Extraction stability on real-world data, rather than accuracy on synthetic benchmarks, is the decisive factor for production LLM deployment.