Factors promoting the stability of animal populations are of perennial interest, having sweeping ramifications for human food security and conservation science. Using a global compilation of feeding surveys for predator species spanning the tree of life, we document notable taxonomic, latitudinal, and temporal scale-dependent patterns in the observed fraction of (non-)feeding individuals. We develop theory to understand the dynamical consequences of these patterns for the tendency of predators to avert extinction, exhibit destabilizing population cycles, and respond resiliently to environmental perturbations. Our predictions of resilience are supported by an independent analysis of empirical population time series. Together, patterns and theory suggest that ongoing environmental changes are weakening the trophic control of prey, increasing predator extinction risks, and decreasing the propensity of predator-prey oscillations.