Modelling the concept of explanation is a central matter in AI systems, as it provides methods for developing eXplainable AI (XAI). When explanation applies to normative reasoning, XAI aims at promoting normative trust in the decisions of AI systems: in fact, such a trust depends on understanding whether systems predictions correspond to legally compliant scenarios. This paper extends to normative reasoning a work by Governatori et al. (2022) on the notion of stable explanations in a non-monotonic setting: when an explanation is stable, it can be used to infer the same normative conclusion independently of other facts that are found afterwards.