The global medical and healthcare industries increasingly rely on technological solutions to address various medical conditions, including epileptic seizures, amid the growing volume of medical data. Epileptic seizures are manifestations of a chronic, noncommunicable brain disorder that can occur spontaneously, often due to genetic abnormalities. This condition can affect individuals of all ages, at any time, and in any setting. The unpredictability of seizure onset poses a significant risk to human health and safety. Deep learning models have demonstrated high accuracy in automating seizure diagnosis in health informatics for seizure diagnosis. However, these models are prone to catastrophic forgetting – the loss of previously acquired knowledge when learning new patterns or data. This study proposes a continual deep learning approach for epileptic seizure prediction using the Bonn University EEG dataset. The model integrates CNN and RNN layers within a continual learning setting to mitigate catastrophic forgetting and enhance knowledge transfer. The proposed model significantly outperformed the baseline models, achieving a weighted F1-score of 0.9234, macro-F1 of 0.8536, misclassification rate of 0.0825, and overall accuracy of 0.9175. In contrast, comparable models without knowledge retention yielded a weighted F1 of 0.9005, macro-F1 of 0.7525, misclassification rate of 0.1202, and accuracy of 0.8583. These findings suggest the potential for real-time clinical applications, including wearable EEG devices and cloud/edge healthcare systems.