DG Tau A, a class-II young stellar object (YSO) displays both thermal,
and non-thermal, radio emission associated with its bipolar jet. To
investigate the nature of this emission, we present sensitive (sigma ~ 2
microJy/beam), Karl G.\ Jansky Very Large Array (VLA) 6 and 10 GHz
observations. Over 3.81 yr, no proper motion is observed towards the
non-thermal radio knot C, previously thought to be a bowshock. Its
quasi-static nature, spatially-resolved variability and offset from the
central jet axis supports a scenario whereby it is instead a stationary
shock driven into the surrounding medium by the jet. Towards the
internal working surface, knot A, we derive an inclination-corrected,
absolute velocity of 258 +/- 23 km/s. DG Tau A's receding counterjet
displays a spatially-resolved increase in flux density, indicating a
variable mass loss event, the first time such an event has been observed
in the counterjet. For this ejection, we measure an ionised mass loss
rate of (3.7 +/- 1.0) * 10**8 Msun/yr during the event. A
contemporaneous ejection in the approaching jet isn't seen, showing it
to be an asymmetric process. Finally, using radiative transfer
modelling, we find that the extent of the radio emission can only be
explained with the presence of shocks, and therefore reionisation, in
the flow. Our modelling highlights the need to consider the relative
angular size of optically thick, and thin, radio emission from a jet, to
the synthesised beam, when deriving its physical conditions from its
spectral index