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. When firms are highly heterogeneous, even small temporary shocks can trigger firm exit and make the economy spiral into a competition-driven poverty trap. We calibrate our model to incorporate the trends on rising firm heterogeneity, and show that they significantly increase the likelihood and length of slow recoveries. (JEL D22, E22, E23, E24, E25, E32)