Autonomous coding agents built on large language models (LLMs) can now solve many general software and machine learning tasks, but they remain ineffective on complex, domain-specific scientific problems. Medical imaging is a particularly demanding domain, requiring long training cycles, high-dimensional data handling, and specialized preprocessing and validation pipelines, capabilities not fully measured in existing agent benchmarks. To address this gap, we introduce ReX-MLE, a benchmark of 20 challenges derived from high-impact medical imaging competitions spanning diverse modalities and task types. Unlike prior ML-agent benchmarks, ReX-MLE evaluates full end-to-end workflows, requiring agents to independently manage data preprocessing, model training, and submission under realistic compute and time constraints. Evaluating state-of-the-art agents (AIDE, ML-Master, R&D-Agent) with different LLM backends (GPT-5, Gemini, Claude), we observe a severe performance gap: most submissions rank in the 0th percentile compared to human experts. Failures stem from domain-knowledge and engineering limitations. ReX-MLE exposes these bottlenecks and provides a foundation for developing domain-aware autonomous AI systems.