Based on a Monte Carlo method, we investigate the influence of transport conditions on the electron spin relaxation in GaAs. The decay of initial electron spin polarization is calculated as a function of distance under the presence of moderate drift fields and/or non-zero injection energies. For relatively low fields (a couple of kV/cm), a substantial amount of spin polarization is preserved for several microns at 300 K. However, it is also found that the spin relaxation rate increases rapidly with the drift field, scaling as the square of the electron wavevector in the direction of the field. When the electrons are injected with a high energy, a pronounced decrease is observed in the spin relaxation length due to an initial increase in the spin precession frequency. Hence, high-field or high-energy transport conditions may not be desirable for spin-based devices.