Firm failures have far-reaching consequences for employees, investors, communities, and the broader economy. Less productive firms are generally more likely to fail. However, high productivity may come at a cost that hampers survival, especially during sudden, unforeseen crises such as COVID-19. Using data from the World Bank Enterprise Survey for small and medium-sized enterprises (SMEs) in 20 European countries, this study tests whether there was a nonlinear association between productivity and survival during the COVID-19 pandemic. The findings suggest that SMEs with below-average productivity relative to their industry were more likely to shut down, whereas firms with exceptionally high productivity do not experience additional survival advantages. These results, while not causal, also hold across alternative SME definitions, underscoring the robustness of the results.