As smart grids evolve to meet growing energy demands and modern operational challenges, the ability to accurately predict faults becomes increasingly critical. However, existing AI-based fault prediction models struggle to ensure reliability in evolving environments where they are required to adapt to new fault types and operational zones. In this paper, we propose a continual learning (CL) framework in the smart grid context to evolve the model together with the environment. We design four realistic evaluation scenarios grounded in class-incremental and domain-incremental learning to emulate evolving grid conditions. We further introduce Prototype-based Dark Experience Replay (ProDER), a unified replay-based approach that integrates prototype-based feature regularization, logit distillation, and a prototype-guided replay memory. ProDER achieves the best performance among tested CL techniques, with only a 0.045 accuracy drop for fault type prediction and 0.015 for fault zone prediction. These results demonstrate the practicality of CL for scalable, real-world fault prediction in smart grids.