A furnace is disclosed that includes a burner with a firing rate that is variable between a minimum and a maximum firing rate. After a call for heat is received, the firing rate is set to an initial level above the minimum firing rate, and the burner is ignited. The firing rate is then modulated downward toward the minimum firing rate. If the flame is lost during or after modulation, the burner is reignited and the firing rate is maintained above the firing rate at which the flame was lost until the current call for heat is satisfied. In some cases, the firing rate is maintained until one or more subsequent calls for heat are satisfied.