The effects of preheating conditions (including the critical energy content, the firing rate, and the equivalence ratio) on the initiation and extinction of a super-adiabatic combustion (SAC) in a steady flow of propane/air mixture through a stack of stainless steel screens (an inert porous medium) are investigated. It is found that there are critical conditions for the initiation and extinction of a SAC in the steady flow through the inert porous column. The critical preheating energy required to initiate a SAC is found to decrease with the increase of the preheating equivalence ratio, the preheating firing rate, and the operational equivalence ratio. After the initiation of a SAC, two combustion modes (i.e., stable combustion mode and push-forward combustion mode) have been observed. These combustion modes are determined by the operational conditions.