Visual prompt-based methods have seen growing interest in incremental learning (IL) for image classification. These approaches learn additional embedding vectors while keeping the model frozen, making them efficient to train. However, no prior work has applied such methods to incremental object detection (IOD), leaving their generalizability unclear. In this paper, we analyze three different prompt-based methods under a complex domain-incremental learning setting. We additionally provide a wide range of reference baselines for comparison. Empirically, we show that the prompt-based approaches we tested underperform in this setting. However, a strong yet practical method, combining visual prompts with replaying a small portion of previous data, achieves the best results. Together with additional experiments on prompt length and initialization, our findings offer valuable insights for advancing prompt-based IL in IOD.