Groups of animals possess phenotypes such as collective behaviour, which may determine the fitness of group members. However, the stability and robustness to perturbations of collective phenotypes in natural conditions is not established. Furthermore, whether group phenotypes are transmitted from parent to offspring groups is required for understanding how selection on group phenotypes contributes to evolution, but parent-offspring resemblance at the group level is rarely estimated. We evaluated robustness to perturbation and parent-offspring resemblance of collective foraging aggressiveness in colonies of the social spider Anelosimus eximius. Among-colony differences in foraging aggressiveness were consistent over time but changed if the colony was perturbed through the removal of individuals, or via their removal and subsequent return. Offspring and parent colony behaviour were correlated, but only once the offspring colony had settled after being translocated. The parent-offspring resemblance was not driven by a shared elevation but could be due to other environmental factors. Laboratory collective behaviour was not correlated with behaviour in the field. Colony aggression seems sensitive to initial conditions and easily perturbed between behavioural states. Despite this sensitivity, offspring colonies have collective behaviour that resembles that of their parent colony, provided they are given enough time to settle into the environment.