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Dynamic benchmarks interweave model fitting and data collection in an attempt to mitigate the limitations of static benchmarks. In contrast to an extensive theoretical and empirical study of the static setting, the dynamic counterpart lags behind due to limited empirical studies and no apparent theoretical foundation to date. Responding to this deficit, we initiate a theoretical study of dynamic benchmarking. We examine two realizations, one capturing current practice and the other modeling more complex settings. In the first model, where data collection and model fitting alternate sequentially, we prove that model performance improves initially but can stall after only three rounds. Label noise arising from, for instance, annotator disagreement leads to even stronger negative results. Our second model generalizes the first to the case where data collection and model fitting have a hierarchical dependency structure. We show that this design guarantees strictly more progress than the first, albeit at a significant increase in complexity. We support our theoretical analysis by simulating dynamic benchmarks on two popular datasets. These results illuminate the benefits and practical limitations of dynamic benchmarking, providing both a theoretical foundation and a causal explanation for observed bottlenecks in empirical work.