  Non-projectable Ho\v{r}ava gravity for a spherically symmetric configuration
with $\lambda=1$ exhibits an infinite set of solutions parametrized by a
generic function $g^{2}(r)$ for the radial component of the shift vector. In
the IR limit the infinite set of solutions corresponds to the invariance of
General Relativity under a spacetime reparametrization. In general, not being a
coordinate transformation, the symmetry in the action responsible for the
infinite set of solutions does not have a clear physical interpretation. Indeed
it is broken by the matter term in the action. We study the behavior of the
solutions for generic values of the parameter $g^{2}(r)$.
