  We consider the extension of the Standard Model (SM) with an inert Higgs
doublet that also contains two or three sets of $SU(2)_L$ triplet fermions with
hypercharge zero and analyze the stability of electroweak vacuum for the
scenarios. The model represents a Type-III inverse seesaw mechanism for
neutrino mass generation with a Dark matter candidate.An effective potential
approach calculation with two-loop beta function have been carried out in
deciding the fate of the electroweak vacuum. Weak gauge coupling $g_2$ shows a
different behaviour as compared to the Standard Model. The modified running of
$g_2$, along with the Higgs quartic coupling and Type-III Yukawa couplings
become crucial in determining the stability of electroweak vacuum. The
interplay between two and three generations of such triplet fermions reveals
that extensions with two generations is favoured if we aspire for Planck scale
stability. Bounds on the Higgs quartic couplings, Type-III Yukawa and number of
triplet fermion generations are drawn for different mass scale of Type-III
fermions. The phenomenologies of inert doublet and Type-III fermions at the LHC
and other experiments are commented upon.
