ABSTRACT 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-energizing 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 ${M}_{\rm {ej}}\lesssim 10^{-2}\, (5\times 10^{-2})\, \mathrm{M}_⊙$, we can rule out very energetic merger ejecta ${E}_{\rm {ej}}\gtrsim 5\times 10^{52}\, (10^{53})\, \rm erg$, thus excluding the presence of a powerful magnetar as a merger remnant.