The video object segmentation (VOS) task involves the segmentation of an object over time based on a single initial mask. Current state-of-the-art approaches use a memory of previously processed frames and rely on matching to estimate segmentation masks of subsequent frames. Lacking any adaptation mechanism, such methods are prone to test-time distribution shifts. This work focuses on matching-based VOS under distribution shifts such as video corruptions, stylization, and sim-to-real transfer. We explore test-time training strategies that are agnostic to the specific task as well as strategies that are designed specifically for VOS. This includes a variant based on mask cycle consistency tailored to matching-based VOS methods. The experimental results on common benchmarks demonstrate that the proposed test-time training yields significant improvements in performance. In particular for the sim-to-real scenario and despite using only a single test video, our approach manages to recover a substantial portion of the performance gain achieved through training on real videos. Additionally, we introduce DAVIS-C, an augmented version of the popular DAVIS test set, featuring extreme distribution shifts like image-/video-level corruptions and stylizations. Our results illustrate that test-time training enhances performance even in these challenging cases.