In this paper, we first discuss the challenges of adapting an already trained DNN-based anomaly detector with knowledge mined during the execution of the main system. Then, we present a framework for the continual learning of anomaly detectors, which records in-field behavioural data to determine what data are appropriate for adaptation. We evaluated our framework to improve an anomaly detector taken from the literature, in the context of misbehavior prediction for self-driving cars. Our results show that our solution can reduce the false positive rate by a large margin and adapt to nominal behaviour changes while maintaining the original anomaly detection capability.