  Studying nonsupersymmetric yet imaginary self-dual three-form fluxes in type
IIB supergravity backgrounds on Sasaki-Einstein manifolds we find a new
analytic solution that restores supersymmetry in the IR, breaks it at higher
energies, yet suffers from curvature singularities in the UV, when a certain
SUSY-breaking parameter becomes large. Consequently we investigate a variety of
possibilities to cure the singularity by either introducing additional sources,
changing the fluxes or deforming the geometry. Since it is not possible to cure
the singularities making physically reasonably assumptions, we suggest that
there might be a no-go theorem disallowing such flux.
