  We study via the renormalization group equations at one-loop order the
perturbativity and vacuum stability of a two-singlet model of cold dark matter
(DM) that consists in extending the Standard Model with two real gauge-singlet
scalar fields. We then investigate the regions in the parameter space in which
the model is viable. For this, we require the model to reproduce the observed
DM relic density abundance, to comply with the measured XENON 100
direct-detection upper bounds, and to be consistent with the RGE perturbativity
and vacuum-stability criteria up to $40\mathrm{TeV}$. For small mixing angle
$\theta $ between the physical Higgs $h$ and auxiliary field, and DM-$h$ mutual
coupling constant $\lambda_{0}^{(4)}$, we find that the auxiliary-field mass is
confined to the interval $116\mathrm{GeV}-138\mathrm{GeV}$ while the DM mass is
mainly confined to the region above $57\mathrm{GeV}$. Increasing $\theta $
enriches the existing viability regions without relocating them, while
increasing $\lambda_{0}^{(4)}$ shrinks them with a tiny relocation. We show
that the model is consistent with the recent Higgs boson-like discovery by the
ATLAS and CMS experiments, while very light dark matter (masses below
$5\mathrm{GeV}$) is ruled out by the same experiments.
