The nature of the progenitor systems and explosion mechanisms that give rise to Type Ia supernovae (SNe Ia) are still debated. The interaction signature of circumstellar material (CSM) being swept up by the expanding ejecta can constrain the type of system from which it was ejected. However, most previous studies have focussed on finding CSM ejected shortly before the SN Ia explosion, which still resides close to the explosion site resulting in short delay times until the interaction starts. We used a sample of 3627 SNe Ia from the Zwicky Transient Facility (ZTF) that were discovered between 2018 and 2020 and searched for interaction signatures greater than 100 days after peak brightness. By binning the late-time light curve data to push the detection limit as deep as possible, we identified potential late-time rebrightening in three SNe Ia (SN 2018grt, SN 2019dlf, and SN 2020tfc). The late-time optical detections occur between 550 and 1450d after peak brightness, have mean absolute r-band magnitudes of -16.4 to -16.8mag, and last up to a few hundred days, which is significantly brighter than the late-time CSM interaction discovered in the prototype, SN 2015cp. The late-time detections in the three objects all occur within 0.8kpc of the host nucleus and are not easily explained by nuclear activity, another transient at a similar sky position, or data quality issues. This is suggestive of environment or specific progenitor characteristics playing a role in the production of potential CSM signatures in these SNe Ia. Through simulating the ZTF survey, we estimate that <0.5 per cent of normal SNe Ia display a late-time (>100d post peak) strong H alpha-dominated CSM interaction. This is equivalent to an absolute rate of 8^+20^_-4_ to 54^+91^_-26_ Gpc^-3^yr^-1^ assuming a constant SN Ia rate of 2.4*10^-5^Mpc^-3^yr^-1^ for z<=0.1. Weaker interaction signatures of Halpha emission, more similar to the strength seen in SN 2015cp, could be more common but are difficult to constrain with our survey depth.