Dynamic surface force measurements of the response of a smectic A to layer normal stress exhibited time dependence for topological events in which single smectic layers were added or removed. Single layer-sized jumps in sample thickness had a rapid component of duration of similar to 1 second that produced most of the change in separation, but that was heralded by a slow precursor acceleration in separation, which began up to a few hundred seconds before. This avalanche-like dynamic signature is consistent with a relaxation mechanism based on the Glaberson-Clem-Bourdon instability of vortex lines (screw dislocations) in the smectic order parameter.