  The central engine of short gamma-ray bursts (sGRBs) is hidden from direct
view, operating at a scale much smaller than that probed by the emitted
radiation. Thus we must infer its origin not only with respect to the formation
of the {\it trigger} - the actual astrophysical configuration that is capable
of powering a sGRB - but also from the consequences that follow from the
various evolutionary pathways that may be involved in producing it. Considering
binary neutron star mergers we critically evaluate, analytically and through
numerical simulations, whether the neutrino-driven wind produced by the newly
formed hyper-massive neutron star can allow the collimated relativistic outflow
that follows its collapse to actually produce a sGRB or not. Upon comparison
with the observed sGRB duration distribution, we find that collapse cannot be
significantly delayed (<=100 ms) before the outflow is choked, thus limiting
the possibility that long-lived hyper-massive remnants can account for these
events. In the case of successful breakthrough of the jet through the
neutrino-driven wind, the energy stored in the cocoon could contribute to the
precursor and extended emission observed in sGRBs.
