  We investigate the vacuum stability and perturbativity of a pseudoscalar
portal dark matter model with a Dirac dark matter (DM) candidate, through the
renormalization group equation analysis at one-loop order. The model has a
particular feature which can evade the direct detection upper bounds measured
by XENON100 and even that from planned experiment XENON1T. We first find the
viable regions in the parameter space which will give rise to correct DM relic
density and comply with the constraints from Higgs physics. We show that for a
given mass of the pseudoscalar, the mixing angle plays no significant role in
the running of the couplings. Then we study the running of the couplings for
various pseudoscalar masses at mixing angle $\theta = 6^\circ$, and find the
scale of validity in terms of the dark coupling, $\lambda_{d}$. Depending on
our choice of the cutoff scale, the resulting viable parameter space will be
determined.
