Approximations introduced in previous calculations of spin relaxation for spin-polarized atomic hydrogen are investigated by carrying out a more exact coupled-channel calculation. With the exception of the high-temperature approximation, the approximations turn out to be justified up to the ${10}^{\ensuremath{-}3}$ level of accuracy. It is shown that at the lowest temperatures for which experimental data are available, the high-temperature limit underestimates relaxation rates by a factor of up to 2. For a comparison with experimental data it is also of interest to pay attention to the expression for the atomic hydrogen relaxation rates in terms of transition amplitudes for two-particle collisions. Discrepancies by a factor of 2 among previous derivations of relaxation rates are pointed out. To shed light on these discrepancies we present two alternative derivations in which special attention is paid to identical-particle aspects. Comparing with experiment, we find our theoretical volume relaxation rate to be in better agreement with measured values than that obtained by other groups. The theoretical surface relaxation rate, however, still shows a discrepancy with experiment by a factor of order 50.