We have experimentally discovered an instability, which manifests itself as precipitations of hot electrons occurring synchronously with generation of bursts of electromagnetic radiation, in the plasma of an electron cyclotron resonance discharge maintained by a high-power, continuous-wave radiation of a 24 GHz gyrotron, for the first time. The observed instability has the kinetic nature and is determined by the formation of the non-equilibrium velocity distribution of hot particles. Two possible explanations are proposed for the mechanism of wave excitation in a two-component plasma with a stationary source of non-equilibrium particles. The results of the studies performed are of interest for modeling of the dynamics of magnetospheric cyclotron masers.