HD 167971 is a triple system consisting of a 3.3-day eclipsing binary (O5-8 V + O5-8 V) and an O8 supergiant. It is also a well known non-thermal radio emitter. We observed the radio emission of HD 167971 with the Very Large Array (VLA) and the Australia Telescope Compact Array (ATCA). By combining these data with VLA archive observations we constructed a radio lightcurve covering a 20-yr time-range. We searched for, but failed to find, the 3.3-day spectroscopic period of the binary in the radio data. This could be due to the absence of intrinsic synchrotron radiation in the colliding-wind region between the two components of the eclipsing binary,or due to the large amount of free-free absorption that blocks the synchrotron radiation. We are able to explain many of the observed characteristics of the radio data if the non-thermal emission is produced in a colliding-wind region between the supergiant and the combined winds of the binary. Furthermore, if the system is gravitationally bound, the orbital motion occurs over a period of ~20 years or longer, as suggested by the long-term variability in the radio data. We argue that the variability is due to the free-free absorption that changes with orbital phase or may also in part be due to changes in separation, should the orbit be eccentric. Table A.1 is only available in electronic form at http://www.aanda.org