We have studied spin dephasing in a high-mobility two-dimensional electron system confined in a GaAs/AlGaAs quantum well grown in the [110] direction, using the resonant spin amplification (RSA) technique. From the characteristic shape of the RSA spectra, we are able to extract the spin dephasing times (SDTs) for electron spins aligned along the growth direction or within the sample plane, as well as the g factor. We observe a strong anisotropy in the spin dephasing times. While the in-plane SDT remains almost constant as the temperature is varied between 4 and 50 K, the out-of-plane SDT shows a dramatic increase at a temperature of about 25 K and reaches values of about 100 ns. The SDTs at 4 K can be further increased by additional, weak above-barrier illumination. The origin of this unexpected behavior is discussed. The SDT enhancement is attributed to the redistribution of charge carriers between the electron gas and remote donors.