Deep learning algorithms for video Snapshot Compressive Imaging (SCI) have achieved great success, yet they predominantly focus on reconstructing from clean measurements. This overlooks a critical real-world challenge: the captured signal itself is often severely degraded by motion blur and low light. Consequently, existing models falter in practical applications. To break this limitation, we pioneer the first study on robust video SCI restoration, shifting the goal from "reconstruction" to "restoration"--recovering the underlying pristine scene from a degraded measurement. To facilitate this new task, we first construct a large-scale benchmark by simulating realistic, continuous degradations on the DAVIS 2017 dataset. Second, we propose RobustSCI, a network that enhances a strong encoder-decoder backbone with a novel RobustCFormer block. This block introduces two parallel branches--a multi-scale deblur branch and a frequency enhancement branch--to explicitly disentangle and remove degradations during the recovery process. Furthermore, we introduce RobustSCI-C (RobustSCI-Cascade), which integrates a pre-trained Lightweight Post-processing Deblurring Network to significantly boost restoration performance with minimal overhead. Extensive experiments demonstrate that our methods outperform all SOTA models on the new degraded testbeds, with additional validation on real-world degraded SCI data confirming their practical effectiveness, elevating SCI from merely reconstructing what is captured to restoring what truly happened.