Two independent types of ab initio calculations for three electrons in the field of a proton have been carried out. Neither calculation shows any evidence for the existence of a resonant state of ${\mathrm{H}}^{2\mathrm{\ensuremath{-}}}$ contributing to e+${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ inelastic scattering, at energies above the three-electron escape threshold. One of the methods used is based on an eigenchannel R-matrix calculation carried out within a reaction volume of finite radius ${\mathit{r}}_{0}$, followed by an averaging procedure over ${\mathit{r}}_{0}$. A second method is based on a configuration-interaction study of the dependence of the 2${\mathit{s}}^{2}$2p $^{2}$${\mathit{P}}^{\mathit{o}}$ resonance on the nuclear charge Z. These calculations suggest that previous experimental and theoretical studies of this system were in erroneous agreement that two $^{2}$${\mathit{P}}^{\mathit{o}}$ resonances exist in ${\mathrm{H}}^{2\mathrm{\ensuremath{-}}}$ above the three-electron escape threshold. We also show that the earlier apparent agreement between experimental and theoretical resonance properties would violate unitarity of the collision matrix.