Photovoltaic (PV) energy grows rapidly and is crucial for the decarbonization of electric systems. However, centralized registries recording the technical characteristifs of rooftop PV systems are often missing, making it difficult to accurately monitor this growth. The lack of monitoring could threaten the integration of PV energy into the grid. To avoid this situation, the remote sensing of rooftop PV systems using deep learning emerged as a promising solution. However, existing techniques are not reliable enough to be used by public authorities or transmission system operators (TSOs) to construct up-to-date statistics on the rooftop PV fleet. The lack of reliability comes from the fact that deep learning models are sensitive to distribution shifts. This work proposes a comprehensive evaluation of the effects of distribution shifts on the classification accuracy of deep learning models trained to detect rooftop PV panels on overhead imagery. We construct a benchmark to isolate the sources of distribution shift and introduce a novel methodology that leverages explainable artificial intelligence (XAI) and decomposition of the input image and model's decision in terms of scales to understand how distribution shifts affect deep learning models. Finally, based on our analysis, we introduce a data augmentation technique meant to improve the robustness of deep learning classifiers to varying acquisition conditions. We show that our proposed approach outperforms competing methods. We discuss some practical recommendations for mapping PV systems using overhead imagery and deep learning models.