There exists a small family of analytic SO(4)-invariant but time-dependent SU(2) Yang–Mills solutions in any conformally flat four-dimensional spacetime. These might play a role in early-universe cosmology for stabilizing the symmetric Higgs vacuum. We analyze the linear stability of these “cosmic gauge fields” against general gauge-field perturbations while keeping the metric frozen, by diagonalizing the (time-dependent) Yang–Mills fluctuation operator around them and applying Floquet theory to its eigenfrequencies and normal modes. Except for the exactly solvable SO(4) singlet perturbation, which is found to be marginally stable linearly but bounded nonlinearly, generic normal modes often grow exponentially due to resonance effects. Even at very high energies, all cosmic Yang–Mills backgrounds are rendered linearly unstable.