The COBRA collaboration operates a demonstrator setup at the underground facility Laboratori Nazionali del Gran Sasso (LNGS, located in Italy) to prove the technological capabilities of this concept for the search for neutrinoless double beta-decay. The setup consists of 64 (1×1×1) cm³ Cadmium-Zinc-Telluride (CZT) detectors in Coplanar-Grid (CPG) configuration. One purpose of this demonstrator is to test if reliable long-term operation of CZT-CPG detectors in such a setup is possible. The demonstrator has been operated under ultra low-background conditions for more than three years and collected data corresponding to a total exposure of 218 kg days. The presented study focuses on the long-term stability of CZT detectors by analyzing the intrinsic, fourfold forbidden non-unique ¹¹³Cd single beta-decay. It can be shown that CZT detectors can be operated stably for long periods of time and that the ¹¹³Cd single beta-decay can be used as an internal monitor of the detector performance during the runtime of the experiment.