Vision-language Models (VLMs), despite achieving strong performance on multimodal benchmarks, often misinterpret straightforward visual concepts that humans identify effortlessly, such as counting, spatial reasoning, and viewpoint understanding. Previous studies manually identified these weaknesses and found that they often stem from deficits in specific skills. However, such manual efforts are costly, unscalable, and subject to human bias, which often overlooks subtle details in favour of salient objects, resulting in an incomplete understanding of a model's vulnerabilities. To address these limitations, we propose a Reinforcement Learning (RL)-based framework to automatically discover the failure modes or blind spots of any ``candidate VLM'' on a given data distribution without human intervention. Our framework trains a questioner agent that adaptively generates queries based on the candidate VLM's responses to elicit incorrect answers. Our approach increases question complexity by focusing on fine-grained visual details and distinct skill compositions as training progresses, consequently identifying novel failure modes in which VLMs struggle. We demonstrate the broad applicability of our framework by showcasing its generalizability across various model combinations.