  Neutron star mergers produce a substantial amount of fast-moving ejecta,
expanding outwardly for years after the merger. The interaction of these ejecta
with the surrounding medium may produce a weak isotropic radio remnant,
detectable in relatively nearby events. We use late-time radio observations of
short duration gamma-ray bursts (sGRBs) to constrain this model. Two samples of
events were studied: four sGRBs that are possibly in the local (<200 Mpc)
universe were selected to constrain the remnant non-thermal emission from the
sub-relativistic ejecta, whereas 17 sGRBs at cosmological distances were used
to constrain the presence of a proto-magnetar central engine, possibly
re-energezing the merger ejecta. We consider the case of GRB~170817A/GW170817,
and find that in this case the early radio emission may be quenched by the jet
blast-wave. In all cases, for ejecta mass range of M_ej \lesssim 10^{-2} (5 *
10^{-2}) M_sun, we can rule out very energetic merger ejecta E_ej \gtrsim 5 *
10^{52}(10^{53}) erg, thus excluding the presence of a powerful magnetar as a
merger remnant.
