  We present a search for nearby (D<100 Mpc) galaxies in the error boxes of six
well-localized short-hard gamma-ray bursts (GRBs). None of the six error boxes
reveals the presence of a plausible nearby host galaxy. This allows us to set
lower limits on the distances and, hence, the isotropic-equivalent energy of
these GRBs. Our lower limits are around $1 \times 10^{49}$ erg (at $2\sigma$
confidence level); as a consequence, some of the short-hard GRBs we examine
would have been detected by BATSE out to distances greater than 1 Gpc and
therefore constitute a bona fide cosmological population. Our search is
partially motivated by the December 27, 2004 hypergiant flare from SGR 1806-20,
and the intriguing possibility that short-hard GRBs are extragalactic events of
a similar nature. Such events would be detectable with BATSE to a distance of
\~50 Mpc, and their detection rate should be comparable to the actual BATSE
detection rate of short-hard GRBs. The failure of our search, by contrast,
suggests that such flares constitute less than 15% of the short-hard GRBs (<40%
at 95% confidence). We discuss possible resolutions of this discrepancy.
