Consider the 3-D cubic NLS with an attractive potential. Our result concerns the stability of the ground state under time periodic perturbations (nonlinear management). We show that, due to a resonant coupling with the radiation, the amplitude of the ground state decays polynomially in time and any solitary waves in the system are eventually destroyed. The result can be viewed as a “second order correction” to the time averaged dynamics which predicts the survival of a solitary wave.