In object detection, unsupervised domain adaptation (UDA) aims to transfer knowledge from a labeled source domain to an unlabeled target domain. However, UDA's reliance on labeled source data restricts its adaptability in privacy-related scenarios. This study focuses on source-free object detection (SFOD), which adapts a source-trained detector to an unlabeled target domain without using labeled source data. Recent advancements in self-training, particularly with the Mean Teacher (MT) framework, show promise for SFOD deployment. However, the absence of source supervision significantly compromises the stability of these approaches. We identify two primary issues, (1) uncontrollable degradation of the teacher model due to inopportune updates from the student model, and (2) the student model's tendency to replicate errors from incorrect pseudo labels, leading to being trapped in a local optimum. Both factors contribute to a detrimental circular dependency, resulting in rapid performance degradation in recent self-training frameworks. To tackle these challenges, we propose the Dynamic Retraining-Updating (DRU) mechanism, which actively manages the student training and teacher updating processes to achieve co-evolutionary training. Additionally, we introduce Historical Student Loss to mitigate the influence of incorrect pseudo labels. Our method achieves state-of-the-art performance in the SFOD setting on multiple domain adaptation benchmarks, comparable to or even surpassing advanced UDA methods. The code will be released soon.