Objective There is an extensive literature analyzing the relationship between democracy and infant mortality; however, findings are mixed. Some studies find a significant inverse relationship, while others conclude that no such relationship exists. We seek to take the debate in a new direction, overlooked in prior research, by providing a theoretical rational for and empirical evidence of a quadratic relationship, in which countries with components of both autocracy and democracy have higher infant mortality. Methods We test lagged, cross‐sectional models on a sample of 47 Sub‐Saharan African nations. Results We find that a quadratic model better explains cross‐national variation in infant mortality than the linear alternative. Infant mortality tends to be higher in hybrid regimes, relative to both autocracies and democracies. Hybrids appear to be politically unstable, which may in part account for their greater infant mortality. Conclusion Hybrid regimes exist in precarious positions with detrimental consequences for population health.