At present, the classification accuracy of high-resolution Remote Sensing Image Scene Classification (RSISC) has reached a quite high level on standard datasets. However, when coming to practical application, the intrinsic noise of satellite sensors and the disturbance of atmospheric environment often degrade real Remote Sensing (RS) images. It introduces defects to them, which affects the performance and reduces the robustness of RSISC methods. Moreover, due to the restriction of memory and power consumption, the methods also need a small number of parameters and fast computing speed to be implemented on small portable systems such as unmanned aerial vehicles. In this paper, a Lightweight Progressive Inpainting Network (LPIN) and a novel combined approach of LPIN and the existing RSISC methods are proposed to improve the robustness of RSISC tasks and satisfy the requirement of methods on portable systems. The defects in real RS images are inpainted by LPIN to provide a purified input for classification. With the combined approach, the classification accuracy on RS images with defects can be improved to the original level of those without defects. The LPIN is designed on the consideration of lightweight model. Measures are adopted to ensure a high gradient transmission efficiency while reducing the number of network parameters. Multiple loss functions are used to get reasonable and realistic inpainting results. Extensive tests of image inpainting of LPIN and classification tests with the combined approach on NWPU-RESISC45, UC Merced Land-Use and AID datasets are carried out which indicate that the LPIN achieves a state-of-the-art inpainting quality with less parameters and a faster inpainting speed. Furthermore, the combined approach keeps the comparable classification accuracy level on RS images with defects as that without defects, which will improve the robustness of high-resolution RSISC tasks.