Recent advances in Multimodal Large Reasoning Models (MLRMs) have enabled explicit chain-of-thought inference across vision and language, substantially improving performance on complex reasoning tasks. Despite these gains, the reasoning process introduces a subtle yet critical vulnerability. We identify an underexplored multimodal safety failure mode in which harmful objectives are embedded within ostensibly benign contexts, leading models to over-prioritize narrative coherence during reasoning. We term this phenomenon Safety Context Amnesia (SCA), wherein models correctly perceive risk-relevant visual cues but fail to enforce safety constraints as the reasoning process becomes dominated by contextual alignment. To mitigate SCA, we propose Intent-Guided Safety Reasoning (IGSR), an inference-time defense that operates without modifying target model parameters. IGSR employs a Perception Decoupler to extract objective visual evidence into a structured intent output, followed by a Cognitive Arbiter that enforces explicit safety constraints prior to generation. Extensive experiments across multiple multimodal safety benchmarks demonstrate that IGSR improves defense success rates by over 62% compared to baselines, while largely preserving task utility. These results highlight the critical role of structured, intent-aware reasoning in achieving robust safety reasoning for multimodal reasoning models.