The unpredictability of seizures continues to distress many people with drug-resistant epilepsy. On account of recent technological advances, considerable efforts have been made using different hardware technologies to realize smart devices for the real-time detection and prediction of seizures. In this paper, we investigate the feasibility of using Memristive Deep Learning Systems (MDLSs) to perform real-time epileptic seizure prediction on the edge. Using the MemTorch simulation framework and the Children's Hospital Boston (CHB)-Massachusetts Institute of Technology (MIT) dataset we determine the performance of various simulated MDLS configurations. An average sensitivity of 77.4% and a Area Under the Receiver Operating Characteristic Curve (AUROC) of 0.85 are reported for the optimal configuration that can process Electroencephalogram (EEG) spectrograms with 7,680 samples in 1.408ms while consuming 0.0133W and occupying an area of 0.1269mm$^2$ in a 65nm Complementary Metal-Oxide-Semiconductor (CMOS) process.