In previous experimental studies it has been observed that the minimum lung pressure to sustain vocal fold oscillation after its onset is lower than the threshold pressure needed to initiate it. This phenomenon is studied analytically using a previous body-cover model of the vocal folds and applying the describing function method to the general case of large amplitude oscillations. It is shown that the phenomenon is a consequence of the nonlinear characteristic of the effective aerodynamic damping introduced by the air pressure acting on the vocal folds. The results predict a value for minimum sustaining pressure equal to half the threshold pressure for a rectangular prephonatory glottis, which is in the order of experimental results.