Real-world tasks are often complex and noisy, posing substantial challenges for LLM agents. Yet existing evaluations lack a systematic framework for jointly characterizing potential perturbation targets and types. We use this two-dimensional view to conduct a unified study that quantifies the robustness of current frontier models, traces the mechanisms behind perturbation-induced failures, and draws implications for robustness-oriented training. Through controlled evaluations on APEX-Agents and Toolathlon, we find that perturbations consistently degrade performance, while the dominant vulnerabilities vary across task environments. Trajectory-level analysis reveals that agents rarely recognize altered inputs and often propagate corrupted information without verification. A focused cost analysis further shows that successful perturbed trajectories can require substantially more computation. These findings motivate training objectives that cover diverse forms of noise and reward verification, uncertainty awareness, and recovery. We provide a rigorous benchmark-construction pipeline. Code and data will be released at https://github.com/xuyj233/AgentPerturb.

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