Anti-D-branes inserted in warped throat geometries (supported by fluxes that carry D-brane charges) develop unphysical singularities.It has been argued that these singularities could be resolved when one goes beyond the linearized approximation or includes the effects of brane polarization.In this paper we consider anti-D6 branes, whose singularities have been shown to exist at the full non-linear level, and demonstrate that there is no D8 brane polarization that can resolve the singularity. We comment on the potential implications of this result for the resolution of anti-D3 brane singularities in the Klebanov-Strassler geometry.