Fault detection is one of the most prominent challenges in the field of multirobot systems (MRS). Most existing fault-tolerant systems prescribe a characterisation of normal behaviours (fault-free behaviours), and train a model to recognise them. Behaviours not recognised by the model are labelled abnormal. MRS employing these models do not transition well to scenarios involving gradual changes in normal behaviour. In such scenarios, existing fault-detection systems may not be applicable, or may incur potentially costly false positive detections. We propose to address this challenging problem by taking inspiration from the regulation of tolerance and (auto)immunity in the adaptive immune system. We deploy an immune system-based fault-detection approach to detect abnormalities in heterogeneously behaving robots. Results of extensive simulation-based experiments demonstrate that a distributed MRS can correctly tolerate delayed propagation of different normal behaviours in the collective, at low false-positive rates. Furthermore, the fault-detection system is able to reliably detect robots performing different fault-simulating behaviours.