The influences of flow stretch, preferential diffusion, internal heat transfer and external heat loss on the extinction of dilute spray flames propagating in a stagnation-point flow are 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 for rich sprays but heat gain for lean sprays. The flow stretch respectively weakens and intensifies the burning intensity of the lean methanol-spray flame (Le > 1) and rich methanol-spray flame (Le < 1). Results show that the Le > 1 flame can be extinguished with or without external heat loss. Flame extinction characterized by a C-shaped curve is dominated by the external heat loss or the flow stretch. For the Le < 1 flame without external heat loss, no extinction occurs under the influence of flow stretch. However, the Le < 1 flame with completely prevaporized fuel sprays enduring a small amount of flow stretch can be extinguished by the external heat loss and this behavior is characterized by a C-shaped curve. Note that the W-shaped extinction curve is mainly governed by the internal heat loss. Flame extinction characterized by a W-shaped curve occurs when the Le < 1 spray flame with external heat loss endures a positive stretch and experiences a partially prevaporized spray with sufficiently large liquid fuel loading and droplet size.