We theoretically study time-dependent correlations in a strongly driven array of $N$ two-level atoms collectively coupled to photons. We focus on the spectrum $\left\{\lambda \right\}$ of the Liouvillian superoperator. Our main finding is the suppression of subradiant oscillating correlations between atomic states by a strong coherent drive: The correlation decay rates $-\mathrm{Re}\lambda$ are lower bounded by thresholds proportional to their oscillation frequencies $\mathrm{Im}\lambda$ and are larger than half of the single-atom decay rate. We demonstrate this limit numerically for various one-, two-, and three-dimensional arrays. In the one-dimensional case of atoms coupled to the waveguide we also provide a rigorous proof based on the analytical decomposition of the Liouvillian using spectral theory of simplicial complexes and partially ordered sets. This limit is independent of the number of atoms $N$; it holds both for small arrays and in the macroscopic limit.

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