This work contains an analysis of the existence of critical phenomena in MILD combustion systems through an exploration of classical results from high-energy asymptotics theory for extinction conditions of non-premixed flames and well-stirred reactors. Through the derivation of an expression linking burning rate to Damköhler number, the criteria for a folded S-Shaped Curve, representative of a combustion system with sudden extinction and ignition behavior, was derived. This theory is discussed in detail, with particular focus on the limitations of the global chemistry it presents. The conditions reported by various previously-published numerical and experimental investigations are then discussed in the context of this theory. Of these investigations, those with the highest level of preheat and dilution had monotonic rather than folded S-Shaped Curves, indicating a lack of sudden extinction phenomena. It suggests that MILD combustion systems are those which lack sudden ignition and extinction behavior, therefore exhibiting a smooth, stretched S-Shaped Curve rather than a folded one with inflection points. The results suggest that the delineation between folded versus monotonic S-Shaped Curves may provide a useful alternative definition of MILD combustion.