  We perform an analysis of the vacuum stability of the neutral scalar
potential of the $\mu$-from-$\nu$ Supersymmetric Standard Model ($\mu\nu$SSM).
As an example scenario, we discuss the alignment-without-decoupling limit of
the $\mu\nu$SSM, for which the required conditions on the Higgs sector are
derived. We demonstrate that in this limit large parts of the parameter space
feature unphysical minima that are deeper than the electroweak minimum. In
order to estimate the lifetime of the electroweak vacuum, we calculate the
rates for the tunneling process into each unphysical minimum. We find that in
many cases the resulting lifetime is longer than the age of the universe, such
that the considered parameter region is not excluded. On the other hand, we
also find parameter regions in which the electroweak vacuum is short-lived. We
investigate how the different regions of stability are related to the presence
of light right-handed sneutrinos. Accordingly, a vacuum stability analysis that
accurately takes into account the possibility of long-lived metastable vacua is
crucial for a reliable assessment of the phenomenological viability of the
parameter space of the $\mu\nu$SSM and its resulting phenomenology at the
(HL)-LHC.
