Theoretical results based on two different modeling approaches indicate that the seismic response of a fault system to steady tectonic loading can exhibit persisting fluctuations in the form of self-driven switching of the response back and forth between two distinct modes of activity. The first mode is associated with clusters of intense seismic activity including the largest possible earthquakes in the system and frequency-size event statistics compatible with the characteristic earthquake distribution. The second mode is characterized by relatively low moment release consisting only of small and intermediate size earthquakes and frequency-size event statistics following a truncated power law. The average duration of each activity mode scales with the time interval of a large earthquake cycle in the system. The results are compatible with various long geologic, paleoseismic, and historical records. The mode switching phenomenon may also exist in responses of other systems with many degrees of freedom and nonlinear dynamics.