Persistent jumps in asset prices are a widely observed phenomenon, yet their underlying causes remain unexplored from a market microstructure perspective. To address this gap, we propose an improved agent-based model incorporating continuous double auctions, which simulates traders' behavior under bounded rationality. Our model generates price series that replicate stylized facts such as leptokurtosis, long-term memory, and heteroscedasticity, while also successfully reproducing frequent persistent jumps, which benchmark models cannot achieve. Sensitivity analysis and model calibration further confirm the robustness of our model, demonstrating that the simulated series are closer to actual financial asset prices compared to benchmark models. Based on our model, the evolution process of agents suggests that the elimination of fundamentalists, under pressure from random traders and chartists, leads to more frequent persistent jumps, providing a possible explanation for the occurrence of persistent jumps and offering new insights for market risk management.