We present the results of a weekly monitoring of the new black hole candidate X-ray binary MAXI J1631-472 carried out with the MeerKAT radio interferometer, the Neil Gehrels Swift Observatory, and the Monitor of All-sky X-ray Image (MAXI) instrument, during its 2018-2019 outburst. The source exhibits a number of X-ray states, in particular both high- and low-luminosity hard states bracketed by extended soft states. Radio flaring is observed shortly after a transition from hard/intermediate states to the soft state. This is broadly in agreement with existing empirical models, but its extended duration hints at multiple unresolved flares and/or jet-ISM interactions. In the hard state radio:X-ray plane, the source is revealed to be radio quiet at high luminosities, but to rejoin the `standard track at lower luminosities, an increasingly commonly-observed pattern of behaviour.