Visible-infrared person re-identification (V-I ReID) seeks to match images of individuals captured over a distributed network of RGB and IR cameras. The task is challenging due to the significant differences between V and I modalities, especially under real-world conditions, where images are corrupted by, e.g, blur, noise, and weather. Indeed, state-of-art V-I ReID models cannot leverage corrupted modality information to sustain a high level of accuracy. In this paper, we propose an efficient model for multimodal V-I ReID -- named Multimodal Middle Stream Fusion (MMSF) -- that preserves modality-specific knowledge for improved robustness to corrupted multimodal images. In addition, three state-of-art attention-based multimodal fusion models are adapted to address corrupted multimodal data in V-I ReID, allowing to dynamically balance each modality importance. Recently, evaluation protocols have been proposed to assess the robustness of ReID models under challenging real-world scenarios. However, these protocols are limited to unimodal V settings. For realistic evaluation of multimodal (and cross-modal) V-I person ReID models, we propose new challenging corrupted datasets for scenarios where V and I cameras are co-located (CL) and not co-located (NCL). Finally, the benefits of our Masking and Local Multimodal Data Augmentation (ML-MDA) strategy are explored to improve the robustness of ReID models to multimodal corruption. Our experiments on clean and corrupted versions of the SYSU-MM01, RegDB, and ThermalWORLD datasets indicate the multimodal V-I ReID models that are more likely to perform well in real-world operational conditions. In particular, our ML-MDA is an important strategy for a V-I person ReID system to sustain high accuracy and robustness when processing corrupted multimodal images. Also, our multimodal ReID model MMSF outperforms every method under CL and NCL camera scenarios.