ABSTRACTWe present an in-depth study of the late-time near-infrared plateau in Type Ia supernovae (SNe Ia), which occurs between 70 and 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 3.5-m 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 ionization 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.