High degree of excitonic spin-state preservation during energy relaxation is demonstrated in a single quantum dot. Optical-phonon resonances and corresponding suppression of spin relaxation are clearly identified as dip structures in photoluminescence excitation spectra probed by the positive trion emission. Consequently, under the longitudinal optical-phonon resonant excitation, a distinguishably high degree of circular polarization up to similar to 0.85 is achieved. Extended spin-relaxation time in the positive trion ground state compared to that in neutral exciton ground state is also revealed.