An extensive dataset for SN 2003hv that covers the flux evolution from maximum light to day +786 is presented. The data are combined with published nebular-phase infrared spectra, and the observations are compared to model light curves and synthetic nebular spectra. SN 2003hv is a normal Type Ia supernova (SN Ia) with photometric and spectroscopic properties consistent with its rarely observed B-band decline-rate parameter, Delta m_15 = 1.61 +- 0.02. The blueshift of the most isolated [Fe II] lines in the nebular-phase optical spectrum appears consistent with those observed in the infrared at similar epochs. At late times there is a prevalent color evolution from the optical toward the near-infrared bands. We present the latest-ever detection of a SN Ia in the near-infrared in Hubble Space Telescope images. The study of the ultraviolet/optical/infrared (UVOIR) light curve reveals that a substantial fraction of the flux is missing at late times. Between 300-700 days past maximum brightness, the UVOIR light curve declines linearly following the decay of radioactive Co56, assuming full and instantaneous positron trapping. At 700 days we detect a possible slowdown of the decline in optical bands, mainly in the V band. The data are incompatible with a dramatic infrared catastrophe. However, the idea that an infrared catastrophe occurred in the densest regions before 350 days can explain the missing flux from the UVOIR wavelengths and the flat-topped profiles in the near-infrared. We argue that such a scenario is possible if the ejecta are clumpy. The observations suggest that positrons are most likely trapped in the ejecta.
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