  The dynamical consistency of the non-projectable version of Horava gravity is
investigated by focusing on the asymptotically flat case. It is argued that for
generic solutions of the constraint equations the lapse must vanish
asymptotically. We then consider particular values of the coupling constants
for which the equations are tractable and in that case we prove that the lapse
must vanish everywhere -- and not only at infinity. Put differently, the
Hamiltonian constraints are generically all second-class. We then argue that
the same feature holds for generic values of the couplings, thus revealing a
physical inconsistency of the theory. In order to cure this pathology, one
might want to introduce further constraints but the resulting theory would then
lose much of the appeal of the original proposal by Horava. We also show that
there is no contradiction with the time reparametrization invariance of the
action, as this invariance is shown to be a so-called "trivial gauge symmetry"
in Horava gravity, hence with no associated first-class constraints.
