We present new radio observations of the binary neutron star merger GW170817 carried out with the Karl G. Jansky Very large Array (VLA) more than 3,yrs after the merger. Our combined dataset is derived by co-adding more than $approx32$,hours of VLA time on-source, and as such provides the deepest combined observation (rms sensitivity $approx 0.99,mu$Jy) of the GW170817 field obtained to date at 3,GHz. We find no evidence for a late-time radio re-brightening at a mean epoch of $tapprox 1200$,d since merger, in contrast to a $approx 2.1,sigma$ excess observed at X-ray wavelengths at the same mean epoch. Our measurements agree with expectations from the post-peak decay of the radio afterglow of the GW170817 structured jet. Using these results, we constrain the parameter space of models that predict a late-time radio re-brightening possibly arising from the high-velocity tail of the GW170817 kilonova ejecta, which would dominate the radio and X-ray emission years after the merger (once the structured jet afterglow fades below detection level). Our results point to a steep energy-speed distribution of the kilonova ejecta (with energy-velocity power law index $alpha gtrsim 5$). We suggest possible implications of our radio analysis, when combined with the recent tentative evidence for a late-time re-brightening in the X-rays, and highlight the need for continued radio-to-X-ray monitoring to test different scenarios.
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