Lithium-sulfur batteries could deliver significantly higher gravimetric energy density and lower cost than Li-ion batteries. Their mass adoption, however, depends on many factors, not least on attaining a predictive understanding of the mechanisms that determine their performance under realistic operational conditions, such as partial charge/discharge cycles. This work addresses a lack of such understanding by studying experimentally and theoretically the response to partial cycling. A lithium-sulfur model is used to analyze the mechanisms dictating the experimentally observed response to partial cycling. The zero-dimensional electrochemical model tracks the time evolution of sulfur species, accounting for two electrochemical reactions, one precipitation/dissolution reaction with nucleation, and shuttle, allowing direct access to the true cell state of charge. The experimentally observed voltage drift is predicted by the model as a result of the interplay between shuttle and the dissolution bottleneck. Other features are shown to be caused by capacity fade. We propose a model of irreversible sulfur loss associated with shuttle, such as caused by reactions on the anode. We find a reversible and an irreversible contribution to the observed capacity fade, and verify experimentally that the reversible component, caused by the dissolution bottleneck, can be recovered through slow charging. This model can be the basis for cycling parameters optimization, or for identifying degradation mechanisms relevant in applications. The model code is released as Supplementary material B.