We have investigated the stability of phase states of single-electron tunneling oscillation phase locked by an external ac pump with twice the tunneling frequency using the Monte Carlo method. It has been shown that the lifetime of phase states depends strongly on the temperature, average current, pump amplitude, and de bias. For a large current, the lifetime is determined by shot noise and decreases drastically with current. For a small current, it is limited by Nyquist noise and increases exponentially with the inverse temperature. Although junctions with a diameter of about 10 nm are required, a lifetime of over 10(4) cycles at 4.2 K can be estimated. We believe that this is a practical value for use in logic processing using phase bistability. (C) 1996 American Institute of Physics.