The optical transient PTF11kx exhibited both the characteristic spectral features of Type Ia supernovae (SNe Ia) and the signature of ejecta interacting with circumstellar material (CSM) containing hydrogen, indicating the presence of a nondegenerate companion. We present an optical spectrum at $1342$ days after peak from Keck Observatory, in which the broad component of H$alpha$ emission persists with a similar profile as in early-time observations. We also present $Spitzer$ IRAC detections obtained $1237$ and $1818$ days after peak, and an upper limit from $HST$ ultraviolet imaging at $2133$ days. We interpret our late-time observations in context with published results - and reinterpret the early-time observations - in order to constrain the CSMs physical parameters and compare to theoretical predictions for recurrent nova systems. We find that the CSMs radial extent may be several times the distance between the star and the CSMs inner edge, and that the CSM column density may be two orders of magnitude lower than previous estimates. We show that the H$alpha$ luminosity decline is similar to other SNe with CSM interaction, and demonstrate how our infrared photometry is evidence for newly formed, collisionally heated dust. We create a model for PTF11kxs late-time CSM interaction and find that X-ray reprocessing by photoionization and recombination cannot reproduce the observed H$alpha$ luminosity, suggesting that the X-rays are thermalized and that H$alpha$ radiates from collisional excitation. Finally, we discuss the implications of our results regarding the progenitor scenario and the geometric properties of the CSM for the PTF11kx system.
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