Large-scale magnetic fields are often observed in the ionosphere of Venus by the magnetometer on the Pioneer Venus Orbiter, especially near the subsolar point or when the solar wind dynamic pressure is high. An equation for the time evolution of the magnetic field is derived which includes both a term representing the time rate of change of the field due the convection of magnetic flux by plasma motions and a magnetic diffusion/dissipation term. The ionosphere plasma velocities required by these equations were obtained by numerically solving the momentum equation. Numerical solutions to the magnetic field equation indicate that large-scale magnetic fields, which are not being actively maintained, decay with time scales ranging from tens of minutes to several hours. The vertical convection of magnetic flux enables magnetic field structures deep within the ionosphere to persist longer than would otherwise be expected. This vertical convection also explains the shape of these structures.