  The anti--de Sitter/conformal field theory (AdS/CFT) correspondence is a
powerful tool that promises to provide new insights toward a full understanding
of field theories under extreme conditions, including but not limited to
quark-gluon plasma, Fermi liquid and superconductor. In many such applications,
one typically models the field theory with asymptotically AdS black holes.
These black holes are subjected to stringy effects that might render them
unstable. Ho\v{r}ava-Lifshitz gravity, in which space and time undergo
different transformations, has attracted attentions due to its power-counting
renormalizability. In terms of AdS/CFT correspondence, Ho\v{r}ava-Lifshitz
black holes might be useful to model holographic superconductors with Lifshitz
scaling symmetry. It is thus interesting to study the stringy stability of
Ho\v{r}ava-Lifshitz black holes in the context of AdS/CFT. We find that
uncharged topological black holes in $\lambda=1$ Ho\v{r}ava-Lifshitz theory are
nonperturbatively stable, unlike their counterparts in Einstein gravity, with
the possible exceptions of negatively curved black holes with detailed balance
parameter $\epsilon$ close to unity. Sufficiently charged flat black holes for
$\epsilon$ close to unity, and sufficiently charged positively curved black
holes with $\epsilon$ close to zero, are also unstable. The implication to the
Ho\v{r}ava-Lifshitz holographic superconductor is discussed.
