GRBs 070429B and 070714B: The High End of the Short-Duration Gamma-Ray Burst Redshift Distribution

We present optical spectra of the host galaxies of the short-duration gamma-ray burst GRB 070429B and the likely short-duration with extended emission GRB 070714B. In both cases, we find a single emission line that we identify as O II lambda 3727 at z ~ 0.9. Both events are more distant than any previous short-duration GRB with a secure host association from the sub-arcsecond position of an optical afterglow. GRBs 070429B and 070714B provide strong evidence in support of our previous claims in Berger et al. that a significant fraction of short-duration hosts (>~ 33%) reside at z > 0.7. We discuss the implications of the existence this population on the energetics of short-duration GRBs, as well as on progenitor models. In the context of the degenerate binary merger scenario, such events require progenitor systems with a range of lifetimes and disfavor progenitor models with a long, narrow lifetime distribution.