In complex ecosystems, the loss of certain species can trigger a cascade of secondary extinctions and invasions. However, our understanding of the prevalence of these critical \"keystone\" species and the factors influencing their emergence remains limited. To address these questions, we experimentally assembled microcosms from 16 marine bacterial species and found that multiple extinctions and invasions were exceedingly rare upon removal of a species from the initial inoculation. This was true across eight different environments with either simple carbon sources (e.g., glucose) and more complex ones (e.g. glycogen). By employing a generalized Lotka-Volterra model, we could reproduce these results when interspecies interactions followed a hierarchical pattern, wherein species impacted strongly by one species were also more likely to experience strong impacts from others. Such a pattern naturally emerges due to observed variation in carrying capacities and growth rates. Furthermore, using both statistical inference and spent media experiments, we inferred interspecies interaction strengths and found them consistent with structured interactions. Our results suggest that the natural emergence of structured interactions may provide community resilience to extinctions.