  We perform a study of the stability of R-parity-conserving vacua of a
constrained version of the minimal supersymmetric model with a gauged
U(1)_{B-L} which can conserve R-parity, using homotopy continuation to find all
the extrema of the tree-level potential, for which we also calculated the
one-loop corrections. While we find that a majority of the points in the
parameter space preserve R-parity, we find that a significant portion of points
which naively have phenomenologically acceptable vacua which conserve R-parity
actually have deeper vacua which break R-parity through sneutrino VEVs. We
investigate under what conditions the deeper R-parity-violating vacua appear.
We find that while previous exploratory work was broadly correct in some of its
qualitative conclusions, we disagree in detail.
