Free-space optical (FSO) communication links are highly sensitive to pointing errors and multi-source disturbances due to the narrow divergence of laser beams, which significantly limits acquisition probability and power coupling efficiency in satellite laser communication systems. Conventional Gaussian beams suffer from rapid performance degradation under pointing bias and angular jitter, motivating the exploration of more robust beam profiles. In this work, the far-field trans-mission characteristics of flat-top Hermite-Gaussian (FHG) beams are systematically investigated under coupled mul-ti-source disturbances, including random phase perturbations, static pointing errors, angular jitter, and defocus. A com-prehensive numerical propagation framework is established to model long-distance free-space transmission over a repre-sentative 500 km LEO optical link, and the statistical coupling efficiency under different effective collection radii is evalu-ated using Monte Carlo simulations. The performance of FHG beams is quantitatively compared with that of fundamental Gaussian beams in terms of mean coupling efficiency, fluctuation range, and pointing-loss sensitivity across different re-ceiver aperture sizes. The results demonstrate that FHG beams exhibit significantly enhanced robustness against point-ing-induced power loss, maintaining higher average coupling efficiency and reduced sensitivity to disturbance strength compared with Gaussian beams. The dependence of performance improvement on receiver aperture size is further ana-lyzed, revealing the practical advantages of FHG beams for disturbance-dominated laser communication links. These findings indicate that flat-top Hermite-Gaussian beams provide an effective physical-layer approach for improving link reliability and acquisition performance in satellite free-space optical communication systems.