We study the temporal development of the Lorentz-force-driven convection in an inhomogeneous magnetic field during copper electrolysis between two vertical electrodes. Using a combination of interferometry and particle image velocimetry we show that the Lorentz-force-driven convection is canceled out even after a moderate duration of the electrolysis. By reversing the current, a re-excitation of the convection is possible which is, however, restricted to a time window of some seconds. The reasons for the decay and re-appearance of the MHD flow are discussed and explained by scaling analysis.