Simulations of forced ignition of non-premixed laminar counterflow flames are used to study the effect of strain rate on ignition success. A one dimensional calculation is performed, using detailed methane chemical kinetics and treating the spark as an instantaneous heat release in an inert mixing layer. Ignition success depends on the mixture composition at the spark location, resulting in lean and rich ignitability limits for a given spark that can be different from the fuel's static flammability limits. The difference is attributed to the finite spark width and the diffusion of heat from the spark to the flammable mixture. Ignition is prohibited by excessive strain rates, in some cases at levels well below the extinction value. The structure of the evolving flame is examined in terms of temperature, heat release rate and species mass fraction distributions. In the case of successful ignition, the high temperature reached due to the spark energy deposition causes local auto-ignition and subsequently, intense burning rapidly consumes the premixed reactants in the mixing layer and a non-premixed flame survives. In the case of unsuccessful ignition, despite the auto-ignition achieved in the sparked region, the strain rate is sufficiently high or the composition is sufficiently far away from the nominally flammable mixture for the heat and radicals to diffuse without resulting in a flame at long times from the spark event.