A spin metal-oxide-semiconductor field-effect transistor (spin MOSFET), which combines a Schottky-barrier MOSFET with ferromagnetic source and drain contacts, is a promising device for spintronic logic. Previous simulation studies predict that this device should display a very high magnetoresistance (MR) ratio (between the cases of parallel and antiparallel magnetizations) for the case of half-metal ferromagnets (HMF). We use the nonequilibrium Green's function formalism to describe tunneling and carrier transport in this device and to incorporate spin relaxation at the HMF-semiconductor interfaces. Spin relaxation at interfaces results in nonideal spin injection. Minority spin currents arise and dominate the leakage current for antiparallel magnetizations. This reduces the MR ratio and sets a practical limit for spin MOSFET performance. We found that MR saturates at a lower value for smaller source-to-drain bias. In addition, spin relaxation at the detector side is found to be more detrimental to MR than that at the injector side, for drain bias less than the energy difference of the minority spin edge and the Fermi level.