The extinction of dilute spray flames propagating in a stagnation-point flow under the influence of flow stretch, preferential diffusion, and internal heat transfer is analyzed using activation energy asymptotics. A completely prevaporized mode and a partially prevaporized mode of flame propagation are identified. The internal heat transfer, associated with the liquid fuel loading and the initial droplet size of the spray, provides heat loss and heat gain for rich and lean sprays, respectively. It is found that the flow stretch coupled with Lewis number (Le) reduces and enhances the burning intensity of the lean methanol-spray flame (Le > 1) and rich methanol-spray flame (Le < 1), respectively, and that the flame extinction characterized by a C-shaped curve for the Le > 1 flame is dominated by the flow stretch, while the S-shaped extinction curve for the Le < 1 flame is mainly influenced by the internal heat loss associated with the droplet gasification process.