The influence of flame stretch, preferential diffusion, internal heat transfer and external heat loss on the extinction of dilute spray flames propagating in a non-adiabatic duct with varying cross-sectional area is analyzed using activation energy asymptotics. A completely prevaporized mode and a partially prevaporized mode of flame propagation are identified. Internal heat transfer, resulting from droplets gasifying, varies with the liquid fuel loading and the initial droplet size in the spray and also provides internal heat loss for rich sprays but heat gain for lean sprays. A spray flame propagating in a divergent (convergent) duct experiences positive (negative) stretch. The results show that the burning intensity of a lean (or rich) spray is enhanced (or reduced) with an increased liquid fuel loading or smaller initial droplets. The positive stretch coupled with the effects of the Lewis number (Le) weakens a lean methanol-spray flame (Le > 1), but intensifies a rich methanol-spray flame (Le < 1). For a positively-stretched flame with Le < 1 or a negatively-stretched flame with Le > 1, if without external heat loss, no extinction occurs by increasing the stretch. However, irrespective of heat loss, a flame with Le > 1 experiencing positive stretch or a flame with Le < 1 enduring negative stretch can be extinguished by increasing the stretch. Flame extinction characterized by a C-shaped curve is dominated by stretch or external heat loss. Note that for a rich methanol spray flame (Le < 1) experiencing positive stretch and enduring a partially prevaporized spray composed of a large enough liquid loading and sufficiently large droplets, an S-shaped extinction curve can be obtained. The S-shaped curve, which differs from the C-shaped one, indicates that flame extinction is governed by internal heat loss.