Food web theory suggests that the placement of a weak interaction is critical such that under some conditions even one well‐placed weak interaction can stabilise multiple strong interactions. This theory suggests that complex stable webs may be built from pivotal weak interactions such that the removal of even one to a few keystone interactions can have significant cascading impacts on whole system diversity and structure. However, the connection between weak interactions, derived from the theory of modular food web components, and keystone species, derived from empirical results, is not yet well understood. Here, we develop numerical techniques to detect potential oscillators hidden in complex food webs, and show that, both in random and real food webs, keystone consumer–resource interactions often operate to stabilise them. Alarmingly, this result suggests that nature frequently may be dangerously close to precipitous change with even the loss of one or a few weakly interacting species.