Robust high-definition (HD) map construction is vital for autonomous driving, yet existing methods often struggle with incomplete multi-view camera data. This paper presents SafeMap, a novel framework specifically designed to secure accuracy even when certain camera views are missing. SafeMap integrates two key components: the Gaussian-based Perspective View Reconstruction (G-PVR) module and the Distillation-based Bird's-Eye-View (BEV) Correction (D-BEVC) module. G-PVR leverages prior knowledge of view importance to dynamically prioritize the most informative regions based on the relationships among available camera views. Furthermore, D-BEVC utilizes panoramic BEV features to correct the BEV representations derived from incomplete observations. Together, these components facilitate the end-to-end map reconstruction and robust HD map generation. SafeMap is easy to implement and integrates seamlessly into existing systems, offering a plug-and-play solution for enhanced robustness. Experimental results demonstrate that SafeMap significantly outperforms previous methods in both complete and incomplete scenarios, highlighting its superior performance and reliability.