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.