Cross-view geo-localization (CVGL) aims to accurately localize street-view images through retrieval of corresponding geo-tagged satellite images. While prior works have achieved nearly perfect performance on certain standard datasets, their robustness in real-world corrupted environments remains under-explored. This oversight causes severe performance degradation or failure when images are affected by corruption such as blur or weather, significantly limiting practical deployment. To address this critical gap, we introduce MRGeo, the first systematic method designed for robust CVGL under corruption. MRGeo employs a hierarchical defense strategy that enhances the intrinsic quality of features and then enforces a robust geometric prior. Its core is the Spatial-Channel Enhancement Block (SCEB), which contains: (1) a Spatial Adaptive Representation Module (SARM) that models global and local features in parallel and uses a dynamic gating mechanism to arbitrate their fusion based on feature reliability; and (2) a Channel Calibration Module (CCM) that performs compensatory adjustments by modeling multi-granularity channel dependencies to counteract information loss. To prevent spatial misalignment under severe corruption, a Region-level Geometric Alignment Module (RGAM) imposes a geometric structure on the final descriptors, ensuring coarse-grained consistency. Comprehensive experiments on both robustness benchmark and standard datasets demonstrate that MRGeo not only achieves an average R@1 improvement of 2.92\% across three comprehensive robustness benchmarks (CVUSA-C-ALL, CVACT_val-C-ALL, and CVACT_test-C-ALL) but also establishes superior performance in cross-area evaluation, thereby demonstrating its robustness and generalization capability.