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The coalescence of a binary neutron star (NS) system may in some casesproduce a massive NS remnant that is long-lived and, potentially, indefinitelystable to gravitational collapse. Such a remnant has been proposed as anexplanation for the late X-ray emission observed following some short durationgamma-ray bursts (GRBs) and as possible electromagnetic counterparts to thegravitational wave chirp. A stable NS merger remnant necessarily possesses alarge rotational energy > 1e52 erg, the majority of which is ultimatelydeposited into the surrounding circumburst medium (CBM) at mildly relativisticvelocities. We present Very Large Array radio observations of 7 short GRBs,some of which possessed temporally extended X-ray emission, on timescales of~1-3 years following the initial burst. No radio sources were detected, withtypical upper limits ~0.3 mJy at 1.4 GHz. A basic model for the synchrotronemission from the blast wave is used to constrain the presence of a long-livedNS merger remnant in each system. Depending on the GRB, our non-detectionstranslate into upper limits on the CBM density n < 3e-2 - 3e-3 particles/cm^3required for consistency with the remnant hypothesis. Our upper limits rule outa long-lived remnant in GRB 050724 and 060505, but cannot rule out such aremnant in other systems due to their lower inferred CBM densities based onafterglow modeling or the lack of such constraints. Additional VLA observationsin the near future could place tighter limits on the presence of mergerremnants in these system. The population of long-lived NS merger remnants willalso be constrained by their (non-)detection with upcoming radio transientsurveys.

Constraints on long-lived remnants of neutron star binary mergers from late-time radio observations of short duration gamma-ray bursts