Do precision electroweak constraints guarantee epem collider discovery of at least one Higgs boson of a type-II two-Higgs-doublet model?

The manner in which the parameters of a two-Higgs-doublet model can be chosen so that no Higgs boson is discovered at a $\sqrt{s}\leq 800\gev$ $\epem$ collider, while maintaining consistency with current precision electroweak measurements, is described. The importance of a Giga-$Z$ factory and higher collider energies for such a scenario is emphasized.