In recent experiments, it has been shown that the switching rate of single-molecule switches can show a rather complicated dependence on the applied bias voltage. Here, we discuss a minimal model which describes the switching process in terms of inelastic scattering processes of the tunneling electron by specific molecular vibrations. One important point is the introduction of an energy-dependent electronic density of states around the Fermi energy. The influence of different model parameters on the switching rate is studied and we show that the inclusion of a variable density of states allows us to understand the non-monotonic behavior of the switching rate observed in some experiments.