Extinction characteristics of hydrogen-air diffusion flames at various pressures are investigated numerically by adopting counterflow flame configuration as a model flamelet. Especially, effect of radiative heat loss on flame extinction is emphasized. Only gas-phase radiation is considered here and it is assumed that $H_2O$ is the only radiating species. Radiation term depends on flame thickness, temperature, $H_2O$ concentration, and pressure. From the calculated flame structures at various pressures, flame thickness decreases with pressure, but its gradient decreases at high pressure. Flame temperature and mole fraction of $H_2O$ increase slightly with pressure. Accordingly, as pressure increases, radiative heat loss becomes dominant. When radiative heat loss is considered, radiation-induced extinction is observed at low strain rate in addition to transport-induced extinction. As pressure increases, flammable region, where flame is sustained, shifts to the high-temperature region and then, shrunk to the point on the coordinate plane of flame temperature and strain rate. The present numerical results show that radiative heat loss can reduce the operating range of a combustor significantly.