Academia provides a valuable case study for evaluating the effects of social forces on workplace productivity, using a concrete measure of output: the scholarly paper. Many academics — especially women — have experienced unprecedented challenges to scholarly productivity with the onset of the COVID-19 pandemic. In this paper, we analyze the gender composition of over 450,000 authorships of scholarly preprints in the preprint repositories arXiv and bioRxiv from before and during the COVID-19 pandemic. This analysis reveals that the underrepresentation of women scientists in the prestige last authorship position necessary for retention and promotion is only getting more inequitable. We find differences between the arXiv and bioRxiv repositories in how gender affects first, middle, and sole authorship submission rates before and during the pandemic. In a second contribution, we review existing research and theory that could explain the mechanisms behind this widening gender gap in productivity during COVID-19. Finally, we aggregate recommendations for institutional change that could help ameliorate challenges to women's productivity during the pandemic and beyond.