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We have imaged over 35 years of archival Very Large Array (VLA) observations of the nearby (d$_{\rm{L}}$ $=$ 3.15 Mpc) Type Ia supernovae SN\,1972E and SN\,1895B between 9 and 121 years post-explosion. No radio emission is detected, constraining the 8.5 GHz luminosities of SN\,1972E and SN\,1895B to be L$_{ν,8.5\rm{GHz}}$ $<$ 6.0 $\times$ 10$^{23}$ erg s$^{-1}$ Hz$^{-1}$ 45 years post-explosion and L$_{ν,8.5\rm{GHz}}$ $<$ 8.9 $\times$ 10$^{23}$ erg s$^{-1}$ Hz$^{-1}$ 121 years post-explosion, respectively. These limits imply a clean circumstellar medium (CSM), with $n$ $<$ 0.9 cm$^{-3}$ out to radii of a few $\times$ 10$^{18}$ cm, if the SN blastwave is expanding into uniform density material. Due to the extensive time coverage of our observations, we also constrain the presence of CSM shells surrounding the progenitor of SN\,1972E. We rule out essentially all medium and thick shells with masses of 0.05$-$0.3 M$_\odot$ at radii between $\sim$10$^{17}$ and 10$^{18}$ cm, and thin shells at specific radii with masses down to $\lesssim$0.01 M$_\odot$. These constraints rule out swaths of parameter space for a range of single and double degenerate progenitor scenarios, including recurrent nova, core-degenerate objects, ultra-prompt explosions and white dwarf (WD) mergers with delays of a few hundred years between the onset of merger and explosion. Allowed progenitors include WD-WD systems with a significant ($>$ 10$^{4}$ years) delay from the last episode of common envelope evolution and single degenerate systems undergoing recurrent nova, provided that the recurrence timescale i short and the system has been in the nova phase for $\gtrsim$10$^{4}$ yr, such that a large ($>$ 10$^{18}$ cm) cavity has been evacuated. Future multi-epoch observations of additional intermediate-aged Type Ia SNe will provide a comprehensive view of the large-scale CSM environments around these explosions.