The effects of strain rate and preferential diffusion of $H_2$ on flame extinction are numerically studied in interacting premixed syngas-air flames with fuel compositions of 50% $H_2$ + 50% CO and 30% $H_2$ + 70% CO. Flame stability diagrams mapping lower and upper limit fuel concentrations at flame extinction as a function of strain rate are examined. Increasing strain rate reduces the boundaries of both flammable lean and rich fuel concentrations and produces a flammable island and subsequently even a point, implying that there exists a limit strain rate over which interacting flame cannot be sustained anymore. Even if effective Lewis numbers are slightly larger than unity on extinction boundaries, the shape of the lean extinction boundary is slanted even at low strain rate, i.e. $a_g=30s^{-1}$ and is more slanted in further increase of strain rate, implying that flame interaction on lean extinction boundary is strong and thus hydrogen (as a deficient reactant) Lewis number much less than unity plays an important role of flame interaction. It is also shown that effects of preferential diffusion of $H_2$ cause flame interaction to be stronger on lean extinction boundaries and weaker on rich extinction boundaries. Detailed analyses are made through the comparison between flame structures with and without the restriction of the diffusivities of $H_2$ and H in symmetric and asymmetric fuel compositions. The reduction of flammable fuel compositions in increase of strain rate suggests that the mechanism of flame extinction is significant conductive heat loss from the stronger flame to ambience.