We study how firm heterogeneity and market power affect macroeconomic fragility, defined as the probability of long slumps. We propose a theory in which the positive interaction between firm entry, competition and factor supply can give rise to multiple steady-states. We show that when firms are highly heterogeneous in terms of productivities, even small temporary shocks can trigger firm exit and make the economy spiral in a competition-driven poverty trap. We calibrate our model to incorporate the well-documented trends on rising firm heterogeneity in the US economy, and show that they significantly increase the likelihood and length of slow recoveries. We use our framework to study the 2008–09 recession and show that the model can rationalize the persistent deviation of output and most macroeconomic aggregates from trend, including the behavior of net entry, markups and the labor share. Post-crisis cross-industry data corroborates our proposed mechanism. We conclude by showing that firm subsidies can be powerful in preventing long slumps and can lead to up to a 21% increase in welfare.