  We show that for the simplest models of gauge mediated supersymmetry
breaking, including all existing models, the true vacuum will not preserve QCD
if it communicates supersymmetry breaking to the visible sector. We show that
the desired supersymmetry breaking color preserving vacuum can nonetheless be
stable cosmologically, but only if certain couplings are sufficiently small. We
also present simple modifications to the sector which communicates
supersymmetry breaking in which the true vacuum is acceptable, suggesting
desirable properties to be sought in dynamical models of supersymmetry
breaking.
