Electron cooling is a fundamental process to guarantee beam quality in low energy antimatter facilities. In ELENA, the electron cooler reduces the emittance blow-up of the antiproton beam so that a focused and bright beam can be delivered to the experiments at the unprecedentedly low energy of 100 keV. To achieve a cold beam at this low energy, the electron gun must emit a monoenergetic and relatively intense electron beam. An optimization of the electron gun involving a cold cathode is studied to investigate the feasibility of using carbon nanotubes (CNTs) as cold electron field emitters. CNTs are considered among the most promising field emitting materials. However, stability data for emission over hundreds of hours, as well as lifetime and conditioning process studies to ensure optimal performance, are still incomplete or missing, especially if the aim is to use them in operation. This contribution reports experiments that characterize these properties and assess whether CNTs are suitable to be used as cold electron field emitters for many hundreds of hours