The heterogeneous reaction SO₂ + H₂O₂ to H₂SO₄ on ice at 228 K has been studied in a low temperature coated-wall flow tube. With H₂O₂ in excess of SO₂, the loss of SO₂ on an ice surface is time dependent with the reaction most efficient on a freshly exposed surface. The deactivation of the surface arises because the protons formed in the reaction inhibit the dissociation of adsorbed SO₂. This lowers the surface concentrations of HSO₃^-, a participant in the rate-determining step of the oxidation mechanism. For a fixed SO₂ partial pressure of 1.4 × 10^-4 Pa, the reaction probabilities for SO₂ loss on a freshly exposed surface scale linearly with H₂O₂ partial pressures between 2.7 × 10^-3 and 2.7 × 10^-2 Pa because the H₂O₂ surface coverage is unsaturated in this regime. Conversely, the reaction probabilities decrease as the partial pressure of SO₂ is raised from 2.7 × 10^-5 to 1.3 × 10^-3 Pa, for a fixed H₂O₂ partial pressure of 8.7 × 10^-3 Pa. This is expected if the rate determining step for the mechanism involves HSO₃^- rather than SO₂. It may also arise to some degree if there is competition between gas phase SO₂ and H₂O₂ for adsorption sites. The reaction is sufficiently fast that the lifetime of SO₂ within ice clouds could be controlled by this heterogeneous reaction and not by the gas-phase reaction with OH.