In this paper, we report on the electrical stability of cadmium telluride (CdTe) detectors with metal-insulator-semiconductor (MIS) structures using a native oxide layer. Although such electrode structures are formed unintentionally owing to oxide formation during electrode processing, few studies have focused on the long-term stability of MIS structures on CdTe detectors. The CdTe detectors fabricated for evaluation were Cu-electrode detectors formed by the surface treatment of the bulk in atmospheric environments and subsequently evaporating copper on it. The fabricated detectors demonstrated excellent rectifying properties after electrical aging, indicating low electrical stability. In addition, their long-term electrical characteristics were unstable, as their properties change with storage. The direction of these changes was not constant, suggesting that the state of the chemical bond between the CdTe surface, the oxide layer, and the copper electrode can evolve, reflecting the multiple bonding possibilities offered by monovalent and divalent copper ions. These results suggest that other metals, including conventional electrode materials, may experience changes in electrode state over time if they are not completely free of a native oxide layer.