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The formalism of complex quasienergies is used for exact calculation of the field-dependent decay rate for a weakly bound particle (in the model of a three-dimensional zero-range potential) in a strong monochromatic laser field. It is shown that the adiabatic (quasistationary) stabilization regime in this model occurs at frequencies ω exceeding the binding energy and only in a limited intensity range. A simple estimate is obtained for the critical field of stabilization breakdown. The effect may be observed for the decay of H– ions in the field of a neodymium laser of femtosecond duration.