Intra-group social stability is important for the long-term productivity and health of social organisms. We evaluated the effect of group size on group stability in the face of repeated social perturbations using a cooperatively breeding fish, Neolamprologus pulcher. In a laboratory study, we compared both the social and physiological responses of individuals from small versus large groups to the repeated removal and replacement of the most dominant group member (the breeder male), either with a new male (treatment condition) or with the same male (control condition). Individuals living in large groups were overall more resistant to instability but were seemingly slower to recover from perturbation. Members of small groups were more vulnerable to instability but recovered faster. Breeder females in smaller groups also showed greater physiological preparedness for instability following social perturbations. In sum, we discover both behavioral and physiological evidence that living in larger groups helps to dampen the impacts of social instability in this system.