  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 CSM's physical
parameters and compare to theoretical predictions for recurrent nova systems.
We find that the CSM's radial extent may be several times the distance between
the star and the CSM's 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 PTF11kx's 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.
