The charge-memory effect, bistability, and switching between charged and neutral states of a molecular junction, as observed in recent scanning-tunneling microscope (STM) experiments, is considered within a minimal polaron model. We show that in the case of strong electron-vibron interaction, the rate of spontaneous quantum switching between charged and neutral states is exponentially suppressed at zero bias voltage but can be tuned through a wide range of finite switching time scales upon changing the bias. We further find that, while junctions with symmetric voltage drop give rise to random switching at finite bias, asymmetric junctions exhibit hysteretic behavior, enabling controlled switching. Lifetimes and charge-voltage curves are calculated by the master-equation method for weak coupling to the leads and at stronger coupling by the equation-of-motion method for nonequilibrium Green's functions.