We study positron annihilation in the resonant state of an exotic three-body system (He(2+) + e(-) + e(+)) by artificially changing a helium nuclear charge and a positron mass. The Ps polarization and non-adiabatic effects on the annihilation are investigated for the lowest broad resonance having an energy width of 3.52 eV. The polarization of Ps due to the nuclear charge and the non-adiabatic effect of the positron make the resonance unstable, and reduce the positron annihilation rate.