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We show how to derive a consistent quantum theory of radiation reaction of a nonrelativistic point-dipole quantum oscillator by including the dynamical fluctuations of the position of the dipole. The proposed nonlinear theory displays neither runaway solutions nor acausal behavior without requiring additional assumptions. Furthermore, we show that quantum (zero-point) fluctuations of the electromagnetic field are necessary to satisfy the second law of thermodynamics. Our results are obtained by developing a nonperturbative technique involving a weak-coupling approximation at the level of the effective action.