  Using ultraviolet (UV) light curves we constrain the circumstellar
environments of 1080 Type Ia supernovae (SNe Ia) within $z<0.5$ from archival
Galaxy Evolution Explorer (GALEX) observations. All SNe Ia are required to have
pre- and post-explosion GALEX observations to ensure adequate subtraction of
the host-galaxy flux. Using the late-time GALEX observations we look for the UV
excess expected from any interaction between the SN ejecta and circumstellar
material (CSM). Four SNe Ia are detected near maximum light and we compare the
GALEX photometry to archival data, but we find none of our targets show
convincing evidence of CSM interaction. A recent Hubble Space Telescope (HST)
survey estimates that $\sim6\%$ of SNe Ia may interact with distant CSM, but
statistical inferences are complicated by the small sample size and selection
effects. By injecting model light curves into our data and then recovering
them, we constrain a broad range of CSM interactions based on the CSM
interaction start time and the maximum luminosity. Combining our GALEX
non-detections with the HST results, we constrain occurrence of late-onset CSM
interaction among SNe Ia with moderate CSM interaction, similar to that
observed in PTF11kx, to $f_\text{CSM}\lesssim5.1\%$ between $0-500$ days after
discovery and $\lesssim2.7\%$ between $500-1000$ days after discovery at $90\%$
confidence. For weaker CSM interactions similar to SN 2015cp, we obtain limits
of $\lesssim16\%$ and $\lesssim4.8\%$, respectively, for the same time ranges.
