Epilepsy, a prevalent neurological disease, demands careful diagnosis and continuous care. However, the detection of epileptic seizures remains a significant challenge. In fact, current clinical practice relies on expert analysis of EEG signals, which is a time-consuming process and requires specialized knowledge. Addressing this challenge, this paper explores the potential for automated epileptic seizure detection using deep learning, with a particular focus on personalized models based on continual learning. We highlight the importance of adapting these models to each patient's unique EEG signal features, which evolve over time. In this context, our approach addresses the fundamental challenge of integrating new data into existing models without losing previously acquired information, a common issue in static deep learning models when applied in dynamic environments. In particular, we propose EpiSMART, a continual learning framework for seizure detection that takes advantage of a size-constrained replay buffer and an informed sample selection strategy to incrementally adapt to patient-specific EEG signals. By selectively retaining high-entropy and seizure-predicted samples, our method preserves critical past information while maintaining high performance with minimal memory and computational overhead. We validate EpiSMART using the CHB-MIT dataset, showing a 21. 33% improvement in the F1 score over a trained baseline without update in all other patients. On average, EpiSMART requires only 6.46 minutes of labeled data and 6.28 updates per day, making it suitable for real-time deployment in wearable systems. These results confirm the effectiveness of our approach in achieving robust and personalized seizure detection under realistic and resource-constrained conditions.