Temporal question answering (TQA) remains a persistent challenge for large language models (LLMs), particularly in retrieval-augmented generation (RAG) settings where retrieved content may be irrelevant, outdated, or temporally inconsistent. This is especially critical in applications like clinical event ordering, policy tracking, and real-time decision-making, which require reliable temporal reasoning even under noisy or misleading context. To address this challenge, we introduce RASTeR: Robust, Agentic, and Structured, Temporal Reasoning, an agentic prompting framework that separates context evaluation from answer generation. RASTeR first assesses the relevance and temporal coherence of retrieved context, then constructs a structured temporal knowledge graph (TKG) to better facilitate reasoning. When inconsistencies are detected, RASTeR selectively corrects or discards context before generating an answer. Across multiple datasets and LLMs, RASTeR consistently improves robustness: defined here as the model's ability to generate correct predictions despite suboptimal context. We further validate our approach through a needle-in-the-haystack'' study, in which relevant context is buried among irrelevant distractors. Even with forty distractors, RASTeR achieves 75% accuracy, compared to the runner-up model, which reaches only 62%.