  We present an in-depth study of the late-time near-infrared plateau in Type
Ia supernovae (SNe Ia), which occurs between 70-500 d. We double the existing
sample of SNe Ia observed during the late-time near-infrared plateau with new
observations taken with the Hubble Space Telescope, Gemini, New Technology
Telescope, the 3.5m Calar Alto Telescope, and the Nordic Optical Telescope. Our
sample consists of 24 nearby SNe Ia at redshift < 0.025. We are able to confirm
that no plateau exists in the Ks band for most normal SNe Ia. SNe Ia with
broader optical light curves at peak tend to have a higher average brightness
on the plateau in J and H, most likely due to a shallower decline in the
preceding 100 d. SNe Ia that are more luminous at peak also show a steeper
decline during the plateau phase in H. We compare our data to state-of-the-art
radiative transfer models of nebular SNe Ia in the near-infrared. We find good
agreement with the sub-Mch model that has reduced non-thermal ionisation rates,
but no physical justification for reducing these rates has yet been proposed.
An analysis of the spectral evolution during the plateau demonstrates that the
ratio of [Fe II] to [Fe III] contribution in a near-infrared filter determines
the light curve evolution in said filter. We find that overluminous SNe decline
slower during the plateau than expected from the trend seen for normal SNe Ia
