Optical enhancement cavities enabling laser pulses to be coherently stacked in free space are used in several applications to enhance accessible optical power. In this study, we develop an optical cavity that accumulates harmonically mode-locked laser pulses with a self-resonating mechanism for X-ray sources based on laser-Compton scattering. In particular, a Fabry-Perot cavity composed of 99% reflectance mirrors maintained the optical resonance in a feedback-free fashion for more than half an hour and automatically resumed the accumulation even if the laser oscillation was suspended. In contrast to conventional optical enhancement cavity systems with a dedicated feedback controller, this characteristic is highly beneficial in practical applications, such as for laser-Compton scattering X-ray sources. Lastly, upscaling and adoption of the proposed system might improve the operability and equipment use of laser Compton-scattering X-ray sources.