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.
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