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 with fidelity 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 the repeatability, 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 individuals’ removal and subsequent return. Offspring and parent colony behaviour were correlated at the phenotypic level, but only once the offspring colony had settled after being translocated, and the correlation overlapped with zero at the among‐colony level. The parent–offspring resemblance was not driven by a shared elevation but could be due to other environmental factors. The behaviour of offspring colonies in a common garden laboratory setting was not correlated with the behaviour of the parent colony nor with the same colony's behaviour once it was returned to the field. The phenotypes of groups represent a potentially important tier of biological organization, and assessing the stability and heritability of such phenotypes helps us better understand their role in evolution.