  It is well-known that the scotogenic model for neutrino mass generation can
explain correctly the relic abundance of cold dark matter. There have been
claims in the literature that an important part of the parameter space of the
simplest scotogentic model can be constrained by the requirement that no
$Z_2$-breaking must occur in the early universe. Here we show that this
requirement does not give any constraints on the underlying parameter space at
least in those parts, where we can trust perturbation theory. To demonstrate
this, we have taken into account the proper decoupling of heavy degrees of
freedom in both, the thermal potential and in the RGE evolution.
