  At bright radio powers ($P_{\rm 1.4 GHz} > 10^{25}$ W/Hz) the space density
of the most powerful sources peaks at higher redshift than that of their weaker
counterparts. This paper establishes whether this luminosity-dependent
evolution persists for sources an order of magnitude fainter than those
previously studied, by measuring the steep--spectrum radio luminosity function
(RLF) across the range $10^{24} < P_{\rm 1.4 GHz} < 10^{28}$ W/Hz, out to high
redshift. A grid-based modelling method is used, in which no assumptions are
made about the RLF shape and high-redshift behaviour. The inputs to the model
are the same as in Rigby et al. (2011): redshift distributions from radio
source samples, together with source counts and determinations of the local
luminosity function. However, to improve coverage of the radio power vs.
redshift plane at the lowest radio powers, a new faint radio sample is
introduced. This covers 0.8 sq. deg., in the Subaru/XMM-Newton Deep Field, to a
1.4 GHz flux density limit of $S_{\rm 1.4 GHz} \geq 100~\mu$Jy, with 99%
redshift completeness. The modelling results show that the previously seen
high-redshift declines in space density persist to $P_{\rm 1.4 GHz} < 10^{25}$
W/Hz. At $P_{\rm 1.4 GHz} > 10^{26}$ W/Hz the redshift of the peak space
density increases with luminosity, whilst at lower radio luminosities the
position of the peak remains constant within the uncertainties. This `cosmic
downsizing' behaviour is found to be similar to that seen at optical
wavelengths for quasars, and is interpreted as representing the transition from
radiatively efficient to inefficient accretion modes in the steep-spectrum
population. This conclusion is supported by constructing simple models for the
space density evolution of these two different radio galaxy classes; these are
able to successfully reproduce the observed variation in peak redshift.
