High degree of preservation of spin states during energy relaxation processes mediated by optical phonons is demonstrated in a single quantum dot. Optical-phonon resonance and relevant suppression of spin relaxation are clearly identified as dip structures in photoluminescence excitation spectra probed by the positive trion emission. The absence of continuum states makes this observation possible under the cross-circularly polarized detection with respect to a circularly polarized pumping. Consequently, distinguishably high degree of circular polarization up to ~0.85 is achieved without applying external magnetic field at the optical-phonon resonance. Rate equation analysis reveals that the spin-flip probability during energy relaxation is restricted to less than 7.5%. It is also indicated that the spin flip time of the positive trion ground state is extended by more than 3 times compared with that of neutral exciton ground state. This corresponds to the spin flip time longer than 11 ns for the positive trion ground state. The influence of nuclear polarization to the present measurements is also discussed.