Plasma of a stationary electron cyclotron resonance (ECR) discharge sustained by gyrotron radiation at a frequency of 24 GHz and a power of up to 300 W in a mirror magnetic trap was studied. At pressures near the gas breakdown threshold, the extinction effect of an electron cyclotron discharge is observed with increasing radiation power. When the cyclotron resonance cross-section approaches the magnetic plug, the power threshold corresponding to the discharge extinction decreases. These experimental results confirm the presence of the effect of particles precipitation from the trap as a result of ECR interaction with gyrotron radiation. The experimental scaling of the extinction power dependence on the position of the ECR cross-section in a magnetic trap corresponds to the results of the estimates on the basis of the theory of particle precipitation in the quasilinear diffusion regime.