  We study the vacuum stability of a minimal Higgs portal model in which the
standard model (SM) particle spectrum is extended to include one complex scalar
field and one Dirac fermion. These new fields are singlets under the SM gauge
group and are charged under a global U(1) symmetry. Breaking of this U(1)
symmetry results in a massless Goldstone boson, a massive CP-even scalar, and
splits the Dirac fermion into two new mass-eigenstates, corresponding to
Majorana fermions. The lightest Majorana fermion (w) is absolutely stable,
providing a plausible dark matter (DM) candidate. We show that interactions
between the Higgs sector and the lightest Majorana fermion which are strong
enough to yield a thermal relic abundance consistent with observation can
easily destabilize the electroweak vacuum or drive the theory into a
non-perturbative regime at an energy scale well below the Planck mass. However,
we also demonstrate that there is a region of the parameter space which
develops a stable vacuum (up to the Planck scale), satisfies the relic
abundance, and is in agreement with direct DM searches. Such an interesting
region of the parameter space corresponds to DM masses 350 GeV \alt m_w \alt 1
TeV. The region of interest is within reach of second generation DM direct
detection experiments.
