Large Language Models face significant challenges in biomedical multi-hop reasoning, including noise interference, context sensitivity, and ensuring factual consistency. To address these limitations, we propose the Robust Biomedical Reasoning Agent (RBRA), a novel agent framework designed to significantly improve the robustness and accuracy of LLMs in this critical domain. RBRA integrates core mechanisms such as hierarchical query decomposition, dynamic context filtering and aggregation, and iterative fact verification and refinement, underpinned by Robustness-aware Metric Optimization. Zero-shot evaluations on BioMultiHopQA-Dynamic, a challenging dataset designed to rigorously assess robustness, confirm its efficacy. RBRA-GPT4o achieves state-of-the-art average accuracy (70.1\%) and robust accuracy (63.5\%). Crucially, RBRA significantly reduces the Robustness Gap to 6.6\% (RBRA-GPT4o) and 6.5\% (RBRA-Llama3-70B), marking a substantial improvement compared to baseline methods' gaps exceeding 12\%. Furthermore, RBRA empowers open-source models, enabling RBRA-Llama3-70B to surpass leading proprietary LLMs in robust accuracy. Ablation studies and detailed analyses confirm the critical contribution of each RBRA component and its superior resilience to various perturbations. RBRA thus represents a significant step towards more reliable and trustworthy AI systems in biomedical applications.