Population persistence has been studied in a conservation context to predict the fate of small or declining populations. Persistence models have explored effects on extinction of random demographic and environmental fluctuations, but in the face of directional environmental change they should also integrate factors affecting whether a population can adapt. Here, we examine the population-size dependence of demographic and genetic factors and their likely contributions to extinction time under scenarios of environmental change. Parameter estimates were derived from experimental populations of the rainforest species, Drosophila birchii, held in the lab for 10 generations at census sizes of 20, 100 and 1000, and later exposed to five generations of heat-knockdown selection. Under a model of directional change in the thermal environment, rapid extinction of populations of size 20 was caused by a combination of low growth rate (r) and high stochasticity in r. Populations of 100 had significantly higher reproductive output, lower stochasticity in r and more additive genetic variance (V(A)) than populations of 20, but they were predicted to persist less well than the largest size class. Even populations of 1000 persisted only a few hundred generations under realistic estimates of environmental change because of low V(A) for heat-knockdown resistance. The experimental results document population-size dependence of demographic and adaptability factors. The simulations illustrate a threshold influence of demographic factors on population persistence, while genetic variance has a more elastic impact on persistence under environmental change.