It was recently predicted [Phys. Rev. B 75, 193301 (2007)] that spin blockade may develop at nonmagnetic semiconductor/perfect ferromagnet junctions when the electron flow is directed from the semiconductor into the ferromagnet. Here we consider current-voltage characteristics of such junctions. By taking into account the contact resistance, we demonstrate a current stabilization effect: by increasing the applied voltage the current density through the junction saturates at a specific value. The transient behavior of the current density is also investigated.