To shorten the operating time of flexible grounding devices in flexible grounding systems, extend their service life, and reduce maintenance costs, it is necessary to provide a fast and accurate judgment basis for their timely withdrawal after fault arc extinction. This paper establishes an equivalent model of grounding faults in flexible grounding systems to analyze the electrical characteristics before and after fault arc extinction. Subsequently, the study investigates SOGI-based filters and frequency-locked loops. Combining these with the characteristic of constant line voltage in distribution network grounding faults, a method for identifying the fault arc extinction moment in flexible grounding systems based on SOGI is proposed. Finally, to verify the effectiveness of the proposed method, a 1007 flexible grounding system simulation model is built using MATLAB/Simulink. The method is validated under various system detuning degrees and transition resistance conditions, demonstrating its good applicability and robustness in accurately identifying the arc extinction moment of grounding faults. The research findings provide a new technical approach for handling grounding faults in distribution networks, with significant engineering application value.