In recent years, Recurrent Spiking Neural Networks (RSNNs) have shown promising potential in long-term temporal modeling. Many studies focus on improving neuron models and also integrate recurrent structures, leveraging their synergistic effects to improve the long-term temporal modeling capabilities of Spiking Neural Networks (SNNs). However, these studies often place an excessive emphasis on the role of neurons, overlooking the importance of analyzing neurons and recurrent structures as an integrated framework. In this work, we consider neurons and recurrent structures as an integrated system and conduct a systematic analysis of gradient propagation along the temporal dimension, revealing a challenging gradient vanishing problem. To address this issue, we propose the Skip Recurrent Connection (SRC) as a replacement for the vanilla recurrent structure, effectively mitigating the gradient vanishing problem and enhancing long-term temporal modeling performance. Additionally, we propose the Adaptive Skip Recurrent Connection (ASRC), a method that can learn the skip span of skip recurrent connection in each layer of the network. Experiments show that replacing the vanilla recurrent structure in RSNN with SRC significantly improves the model's performance on temporal benchmark datasets. Moreover, ASRC-SNN outperforms SRC-SNN in terms of temporal modeling capabilities and robustness.