Efficient persistent monitoring in dynamic environments using multiple Unmanned Aerial Vehicles (UAVs) is essential for various applications. The complexity of this task is heightened by factors such as time-varying environmental states, limited energy capacity, and constrained communication ranges. This paper introduces IRADA (Integrated Reward Aggregation for Distributed Allocation), a novel distributed task allocation method for multi-UAV persistent monitoring in dynamic environments aims to maintain up-to-date situational awareness by minimizing information uncertainty across distributed points of interest (POIs). The decision-making of each UAV is guided by real-time reward of POIs computed in a distributed manner. These rewards integrate information collection efficiency, operational range under energy constraints, and communication tendencies with other UAVs. Furthermore, the integrated rewards are spatially aggregated using Gaussian Mixture Model (GMM) to enhance multi-step decision-making capabilities in a computationally efficient way. Extensive simulations demonstrate that our approach achieves superior performance in rapid information collection across various system configurations, including different numbers of UAVs, travel budgets, and communication ranges, under varying numbers of POIs. Ablation studies validate the advantages of GMM-based reward aggregation in both performance and computational efficiency. Additionally, our method exhibits system resilience when facing UAV failures, maintaining effective coverage through autonomous task redistribution.