We document that 85% of patent applications in the United States include no female inventors and ask: why are women underrepresented in innovation? We argue that differences in responses to early rejections between men and women are a significant contributor to the gender disparity in innovation. We evaluate the prosecution and outcomes of almost one million patent applications in the United States from 2001 through 2012 and leverage variation in patent examiners' probabilities of rejecting applications to employ a quasi-experimental instrumental variables approach. Our results show that applications from women are less likely to continue in the patent process after receiving an early rejection. Roughly half of the overall gender gap in awarded patents during this period can be accounted for by the differential propensity of women to abandon applications. We also provide evidence that the gender gap in persistence is reduced when women-led applications have the backing of firms, consistent with a potential role for institutional support in mitigating gender disparities.