We report clear observation of a high voltage (HV) threshold for stable operation in a dc electron gun. The HV hold-off time without any discharge is longer than many hours for operation below the threshold, while it is roughly 10 min above the threshold. The HV threshold corresponds to the minimum voltage where discharge ceases. The threshold increases with the number of discharges during HV conditioning of the gun. Above the threshold, the amount of gas desorption per discharge increases linearly with the voltage difference from the threshold. The present experimental observations can be explained by an avalanche discharge model based on the interplay between electron stimulated desorption (ESD) from the anode surface and subsequent secondary electron emission from the cathode by the impact of ionic components of the ESD molecules or atoms.