Continuous-time dynamic graph modeling is a crucial task for many real-world applications, such as financial risk management and fraud detection. Though existing dynamic graph modeling methods have achieved satisfactory results, they still suffer from three key limitations, hindering their scalability and further applicability. i) Indiscriminate updating. For incoming edges, existing methods would indiscriminately deal with them, which may lead to more time consumption and unexpected noisy information. ii) Ineffective node-wise long-term modeling. They heavily rely on recurrent neural networks (RNNs) as a backbone, which has been demonstrated to be incapable of fully capturing node-wise long-term dependencies in event sequences. iii) Neglect of re-occurrence patterns. Dynamic graphs involve the repeated occurrence of neighbors that indicates their importance, which is disappointedly neglected by existing methods. In this paper, we present iLoRE, a novel dynamic graph modeling method with instant node-wise Long-term modeling and Re-occurrence preservation. To overcome the indiscriminate updating issue, we introduce the Adaptive Short-term Updater module that will automatically discard the useless or noisy edges, ensuring iLoRE's effectiveness and instant ability. We further propose the Long-term Updater to realize more effective node-wise long-term modeling, where we innovatively propose the Identity Attention mechanism to empower a Transformer-based updater, bypassing the limited effectiveness of typical RNN-dominated designs. Finally, the crucial re-occurrence patterns are also encoded into a graph module for informative representation learning, which will further improve the expressiveness of our method. Our experimental results on real-world datasets demonstrate the effectiveness of our iLoRE for dynamic graph modeling.