Large Language Model (LLM) agents remain vulnerable to safety threats from the external environment, where attackers inject adversarial content into external observations such as tool-returned data, webpages, or MCP context, causing harmful agentic behaviors such as unsafe actions or incorrect outputs. Existing studies typically focus on single-interaction attacks, where the agent observes adversarial content and immediately exhibits harmful behavior within one user request. However, we show that adversarial content can also persist across interactions served by the same agent, making such threats harder to detect and mitigate. Specifically, adversarial content may persist in the agent state, remain dormant across interactions, and later be activated by a benign user query. We formalize this type of safety threat as Sleeper Attack. To evaluate it, we construct a benchmark with 1,896 instances covering six real-world harmful outcomes, three attack strategies, and three agent state targets: session context, memory, and reusable skills. Experiments on seven strong open-source and closed-source LLMs show that state-of-the-art LLM agents remain vulnerable to Sleeper Attack, even when they achieve low attack success rates under a single-interaction baseline. Our code and data are available at https://anonymous.4open.science/r/skdvnfu23ihr9wdscnksf1asdffsaef.