In the multi-turn interaction schema, large language models (LLMs) can leverage user feedback to enhance the quality and relevance of their responses. However, evaluating an LLM's ability to incorporate user refutation feedback is crucial yet challenging. In this study, we introduce RefuteBench 2.0, which significantly extends the original RefuteBench by incorporating LLM agents as refuters and evaluators, which allows for flexible and comprehensive assessment. We design both transient and persistent refutation instructions with different validity periods. Meta-evaluation shows that the LLM-based refuter could generate more human-like refutations and the evaluators could assign scores with high correlation with humans. Experimental results of various LLMs show that current models could effectively satisfy the refutation but fail to memorize the refutation information. Interestingly, we also observe that the performance of the initial task decreases as the refutations increase. Analysis of the attention scores further shows a potential weakness of current LLMs: they struggle to retain and correctly use previous information during long context dialogues. https://github.com/ElliottYan/RefuteBench-2.0