  We study the stability of vacua with spontaneously broken supersymmetry in
N=2 supergravity theories with only hypermultiplets. Focusing on the projection
of the scalar mass matrix along the sGoldstino directions, we are able to
derive a universal upper bound on the lowest mass eigenvalue. This bound only
depends on the gravitino mass and the cosmological constant, but not on the
details of the quaternionic manifold spanned by the scalar fields. Comparing
with the Breitenlohner-Freedman bound shows that metastability requires the
cosmological constant to be smaller than a certain negative critical value.
Therefore, only AdS vacua with a sufficiently negative cosmological constant
can be stable, while Minkowski and dS vacua necessarily have a tachyonic
direction.
