Large language model (LLM) agents increasingly rely on external tools and retrieval systems to autonomously complete complex tasks. However, this design exposes agents to indirect prompt injection (IPI), where attacker-controlled context embedded in tool outputs or retrieved content silently steers agent actions away from user intent. Unlike prompt-based attacks, IPI unfolds over multi-turn trajectories, making malicious control difficult to disentangle from legitimate task execution. Existing inference-time defenses primarily rely on heuristic detection and conservative blocking of high-risk actions, which can prematurely terminate workflows or broadly suppress tool usage under ambiguous multi-turn scenarios. We propose AgentSentry, a novel inference-time detection and mitigation framework for tool-augmented LLM agents. To the best of our knowledge, AgentSentry is the first inference-time defense to model multi-turn IPI as a temporal causal takeover. It localizes takeover points via controlled counterfactual re-executions at tool-return boundaries and enables safe continuation through causally guided context purification that removes attack-induced deviations while preserving task-relevant evidence. We evaluate AgentSentry on the \textsc{AgentDojo} benchmark across four task suites, three IPI attack families, and multiple black-box LLMs. AgentSentry eliminates successful attacks and maintains strong utility under attack, achieving an average Utility Under Attack (UA) of 74.55 %, improving UA by 20.8 to 33.6 percentage points over the strongest baselines without degrading benign performance.