The inelastic lifetimes of electrons in image-potential states at Cu(100) that are Stark-shifted by the electrostatic tip-sample interaction in the scanning tunneling microscope are calculated using the many-body GW approximation. The results demonstrate that in typical tunneling conditions the image state lifetimes are significantly reduced from their field-free values. The Stark-shift to higher energies increases the number of inelastic scattering channels that are available for decay, with field-induced changes in the image state wave function increasing the efficiency of the inelastic scattering through greater overlap with final state wave functions.