An experimental method is developed for the robust frequency stabilization using a high-finesse cavity when the laser exhibits large intermittent frequency jumps. This is accomplished by applying an additional slow feedback signal from Doppler-free fluorescence spectroscopy in an atomic beam with increased frequency locking range. As a result, a stable and narrow-linewidth 556 nm laser maintains the frequency lock status for more than a week, and contributes to more accurate evaluation of the Yb optical lattice clock. In addition, the reference optical cavity is supported at vibration-insensitive points without any vibration isolation table, making the laser setup more simple and compact.