Despite their success, vision transformers still remain vulnerable to image corruptions, such as noise or blur. Indeed, we find that the vulnerability mainly stems from the unstable self-attention mechanism, which is inherently built upon patch-based inputs and often becomes overly sensitive to the corruptions across patches. For example, when we only occlude a small number of patches with random noise (e.g., 10%), these patch corruptions would lead to severe accuracy drops and greatly distract intermediate attention layers. To address this, we propose a new training method that improves the robustness of transformers from a new perspective -- reducing sensitivity to patch corruptions (RSPC). Specifically, we first identify and occlude/corrupt the most vulnerable patches and then explicitly reduce sensitivity to them by aligning the intermediate features between clean and corrupted examples. We highlight that the construction of patch corruptions is learned adversarially to the following feature alignment process, which is particularly effective and essentially different from existing methods. In experiments, our RSPC greatly improves the stability of attention layers and consistently yields better robustness on various benchmarks, including CIFAR-10/100-C, ImageNet-A, ImageNet-C, and ImageNet-P.