  We present results from the first radio observations of a complete orbit (~
17 days) of the neutron star X-ray binary Circinus X-1 using the Australia
Telescope Compact Array Broadband Backend, taken while the system was in an
historically faint state. We have captured the rapid rise and decline of a
periastron passage flare, with flux densities for 9 days prior to the event
stable at ~ 1 mJy at 5.5 GHz and ~ 0.5 mJy at 9 GHz. The highest flux densities
of 43.0 +/- 0.5 mJy at 5.5 GHz and 29.9 +/- 0.6 mJy at 9 GHz were measured
during the flare's decline (MJD 55206.69) which continues towards pre-flare
flux densities over the following 6 days. Imaging of pre-flare data reveals
steady structure including two stable components within 15 arc-seconds of the
core which we believe may be persistent emission regions within the system's
outflows, one of which is likely associated with the system's counter-jet.
Unlike past observations carried out in the system's brighter epochs, we
observe no significant structural variations within \approx 3 arc-seconds of
the core's position. Model subtraction and difference mapping provide evidence
for variations slightly further from the core: up to 5" away. If related to the
observed core flare, then these variations suggest very high outflow velocities
with {\Gamma} > 35, though this can be reduced significantly if we invoke phase
delays of at least one orbital period. Interestingly, the strongest structural
variations appear to the north west of the core, opposite to the strongest
arcsec-scale emission historically. We discuss the implications of this
behaviour, including the possibility of precession or a kinked approaching jet.
