  Aql X-1 is one of the best-studied neutron star low-mass X-ray binaries. It
was previously targeted using quasi-simultaneous radio and X-ray observations
during at least 7 different accretion outbursts. Such observations allow us to
probe the interplay between accretion inflow (X-ray) and jet outflow (radio).
Thus far, these combined observations have only covered one order of magnitude
in radio and X-ray luminosity range; this means that any potential radio -
X-ray luminosity correlation, $L_R \propto L_X^{\beta}$, is not well
constrained ($\beta \approx$ 0.4-0.9, based on various studies) or understood.
Here we present quasi-simultaneous Very Large Array and Swift-XRT observations
of Aql X-1's 2016 outburst, with which we probe one order of magnitude fainter
in radio and X-ray luminosity compared to previous studies ($6 \times 10^{34} <
L_X < 3 \times 10^{35}$ erg s$^{-1}$, i.e., the intermediate to low-luminosity
regime between outburst peak and quiescence). The resulting radio
non-detections indicate that Aql X-1's radio emission decays more rapidly at
low X-ray luminosities than previously assumed - at least during the 2016
outburst. Assuming similar behaviour between outbursts, and combining all
available data, this can be modelled as a steep $\beta=1.17^{+0.30}_{-0.21}$
power-law index or as a sharp radio cut-off at $L_X \lesssim 5 \times 10^{35}$
erg s$^{-1}$ (given our deep radio upper limits at X-ray luminosities below
this value). We discuss these results in the context of other similar studies.
