With the widespread use of large language models (LLMs), understanding their potential failure modes during user interactions is essential. In practice, users often pose multiple questions in a single conversation with LLMs. Therefore, in this study, we propose Group Query Attack, a technique that simulates this scenario by presenting groups of queries to LLMs simultaneously. We investigate how the accumulated context from consecutive prompts influences the outputs of LLMs. Specifically, we observe that Group Query Attack significantly degrades the performance of models fine-tuned on specific tasks. Moreover, we demonstrate that Group Query Attack induces a risk of triggering potential backdoors of LLMs. Besides, Group Query Attack is also effective in tasks involving reasoning, such as mathematical reasoning and code generation for pre-trained and aligned models.