Despite the remarkable success of multi-modal bird's-eye view (BEV) perception in autonomous driving, current systems exhibit a critical vulnerability: existing fusion mechanisms are highly brittle to sensor corruptions, often causing catastrophic performance degradation. This vulnerability largely stems from the fact that standard fusion frameworks typically integrate multi-modal representations in a static manner, leading to a precipitous performance collapse under missing or corrupted modalities. In contrast, we show that graceful degradation is achievable through active modality reliability assessment. To this end, we present Grace-BEV, a lightweight and plug-and-play framework that enforces active reliability awareness during multi-modal fusion. Instead of relying on computationally expensive cross-modal interactions, Grace-BEV leverages the aligned BEV space to explicitly assess modality trustworthiness via a TrustGate Router and dynamically recalibrate feature integration using the FailSafe Fusion Block. Furthermore, we devise a Three-Phase Training strategy with Modality Dropout to prevent modality dominance and encourage balanced cross-modal learning under unreliable inputs. Extensive experiments on nuScenes-R and nuScenes-C show that Grace-BEV maintains robust performance across diverse corruption settings. Notably, under catastrophic LiDAR failures where standard baselines collapse to 0.0% mean Average Precision (mAP), Grace-BEV restores performance to as high as 34.7% mAP. Moreover, it improves clean accuracy by up to 1.4%, achieving a strong trade-off between robustness and efficiency.