  The origin of the low luminosity radio emission in radio-quiet AGN, is
unknown. The detection of a positive correlation between the radio and X-ray
emission would imply a jet-like origin, similar to that seen in `hard state'
X-ray binary systems. In our previous work, we found no believable radio
variability in the well known X-ray bright Seyfert 1 galaxy NGC 4051, despite
large amplitude X-ray variability. In this study we have carefully re-analysed
radio and X-ray observations using the same methods as our previous work, we
again find no evidence for core radio variability. In direct contrast to our
findings, another study claim significant radio variability and a distinctive
anti-correlation between radio and X-ray data for the same source. The other
study report only integral flux values and do not consider the effect of the
changing array on the synthesised beam. In both our studies of NGC 4051 we have
taken great care to account for the effect that the changing beam size has on
the measured radio flux and as a result we are confident that our method gives
more accurate values for the intrinsic core radio flux. However, the lack of
radio variability we find is hard to reconcile because radio images of NGC 4051
do show jet-like structure. We suggest that the radio structures observed are
likely the result of a previous period of higher radio activity and that the
current level of radio emission from a compact nuclear jet is low.
