The recently discovered positronic molecule e+H- 2 [J. Charry et al., Angew. Chem., Int. Ed. 57, 8859-8864 (2018)] has a new type of bond, the single-positron bond. We studied its stability using quantum Monte Carlo techniques. We computed an accurate potential energy curve of the reaction H- + PsH → e+H- 2 → H2 + Ps- to establish its global stability with respect to all possible dissociation channels and to define the range of its local stability. We showed that the e+H- 2 system is stable with respect to the dissociation into H- + PsH, with a binding energy of 23.5(1) mhartree. For R < 3.2 bohrs, the system is unstable, and it decays into H2 + Ps-. There are no other bound structures for R < 3.2 bohrs. We discuss possible routes to its experimental production.