  We present archival and ground-based infrared observations of the
gamma-ray-emitting nova V959 Mon, covering the period 100-4205 days after the
2012 eruption. We use these data to determine that the secondary in the nova
system is a G5 main sequence star. Data from the NEOWISE survey reveal a
significant increase in the emission at 3.4 microns and 4.6 microns at late
(>~600 days) times, which we interpret as emission by dust. Other
interpretations are considered but cannot be reconciled with the data. The
presence of such late dust emission, and in particular its variation with time,
are unprecedented in the context of novae. The behaviour of the dust emission
suggests a qualitative interpretation in which ejecta from the 2012 eruption
encounter denser pre-eruption circumbinary material, giving rise to
Rayleigh-Taylor instabilities that cause clumps of dust-bearing material to
fall back towards the central binary, the dust undergoing destruction by
chemisputtering as it does so. The observed rise in the dust temperature, the
decline in the nova-dust distance and in the dust mass, are consistent with
this interpretation. Not all novae are expected to show this behaviour, but
inspection of resources such as NEOWISE might reveal other novae post-eruption
that do.
