We examine the behaviour of the infrared-radio correlation (IRRC) over the range 0 <z ≲ 6 using new, highly sensitive 3 GHz observations with the Karl G. Jansky Very Large Array (VLA) and infrared data from the Herschel Space Observatory in the 2 deg2 COSMOS field. We distinguish between objects where emission is believed to arise solely from star-formation, and those where an active galactic nucleus (AGN) is thought to be present. We account for non-detections in the radio or in the infrared using a doubly-censored survival analysis. We find that the IRRC of star-forming galaxies, quantified by the infrared-to-1.4 GHz radio luminosity ratio (qTIR), decreases with increasing redshift: qTIR(z) = (2.88 ± 0.03)(1 + z)− 0.19 ± 0.01. This is consistent with several previous results from the literature. Moderate-to-high radiative luminosity AGN do not follow the same qTIR(z) trend as star-forming galaxies, having a lower normalisation and steeper decrease with redshift. We cannot rule out the possibility that unidentified AGN contributions only to the radio regime may be steepening the observed qTIR(z) trend of the star-forming galaxy population. We demonstrate that the choice of the average radio spectral index directly affects the normalisation, as well as the derived trend with redshift of the IRRC. An increasing fractional contribution to the observed 3 GHz flux by free-free emission of star-forming galaxies may also affect the derived evolution. However, we find that the standard (M82-based) assumption of the typical radio spectral energy distribution (SED) for star-forming galaxies is inconsistent with our results. This suggests a more complex shape of the typical radio SED for star-forming galaxies, and that imperfect K corrections in the radio may govern the derived trend of decreasing qTIR with increasing redshift. A more detailed understanding of the radio spectrum is therefore required for robust K corrections in the radio and to fully understand the cosmic evolution of the IRRC. Lastly, we present a redshift-dependent relation between rest-frame 1.4 GHz radio luminosity and star formation rate taking the derived redshift trend into account.