The Heavy Ion Research Facility in Lanzhou is a significant acceleration system providing beams of ions from hydrogen to uranium. During operational cycles, periodic beam loss has been observed in the Cooler Storage Ring, prompting an investigation into its root causes. Our study began with an analysis of the ripple currents in the analog dipole magnet power supply and the associated magnetic field fluctuations. Through combined experimental measurements and numerical simulations, we confirmed that magnetic field jitter induced orbit distortion, which perturbed beam phase and triggered longitudinal parametric resonance. When the modulation tune approaches the bifurcation tune during acceleration cycles, the particles in the outer beamlet can escape from the RF bucket and beam loss occurs. To address this issue while simultaneously increasing the ramping rate of the dipole magnetic field, we replaced the legacy analog power supply with a digital one. The ripple spectrum of the new power supply is dominated by a component at 5000 Hz, which is significantly higher than the synchronous frequency. Furthermore, the relative amplitude deviation of the current, defined as the ratio of the ripple amplitude to the nominal current, was reduced from $9.03\times {10}^{-4}$ to $1.25\times {10}^{-4}$, the modulation tune remains well above the bifurcation tune without intersection throughout the acceleration. Consequently, the longitudinal parametric resonance is eliminated and beam loss is significantly reduced during beam commissioning. The findings provide valuable insights for the optimization of similar accelerator facilities.