Observations from the Pioneer Venus Orbiter magnetometer suggest that a large-scale magnetic field is induced in the dayside ionosphere when the solar wind dynamic pressure is high. The presistance of the large-scale field structure is investigated by using realistic models of the neutral atmosphere and ionosphere. Under the assumptions that the magnetic field is horizontal with vertical gradients, the magnetic field evolution is described by a diffusion-convective equation where the diffusion coefficient depends on the sum of the electron-neutral and electron-ion collision frequencies. In this one-dimensional model the diffusion coefficient and the vertical plasma drift velocity together determine the time scale for the field disappearance. Numerical solutions of the field equation suggest that a large-scale field in the dayside Venus ionosphere disappears with a time scale of minutes for a vertical velocity of ~10 m/s, but that the lifetime increases to several hours if the vertical velocity is small. Above ~200 km altitude, the observed antisolar convection of the ionospheric plasma would cause the field to diminish more rapdily then these diffusion time scales, but at lower altitudes the diffusion process determines the rate of field decay. This result may explain somf of the observations of quasi-steady, large-scale magnetic fields in the Venus ionosphere during steady solar wind conditions as remnants of field previously induced by the solar wind interactions.