Diffusion models have demonstrated exceptional capabilities in image restoration, yet their application to video super-resolution (VSR) faces significant challenges in balancing fidelity with temporal consistency. Our evaluation reveals a critical gap: existing approaches consistently fail on severely degraded videos--precisely where diffusion models' generative capabilities are most needed. We identify that existing diffusion-based VSR methods struggle primarily because they face an overwhelming learning burden: simultaneously modeling complex degradation distributions, content representations, and temporal relationships with limited high-quality training data. To address this fundamental challenge, we present DiffVSR, featuring a Progressive Learning Strategy (PLS) that systematically decomposes this learning burden through staged training, enabling superior performance on complex degradations. Our framework additionally incorporates an Interweaved Latent Transition (ILT) technique that maintains competitive temporal consistency without additional training overhead. Experiments demonstrate that our approach excels in scenarios where competing methods struggle, particularly on severely degraded videos. Our work reveals that addressing the learning strategy, rather than focusing solely on architectural complexity, is the critical path toward robust real-world video super-resolution with diffusion models.