I know of no such event and I would be very surprised if there was one, not least since the Sasanian Empire wasn't as tolerant as many assume, nor were pagans as persecuted in Rome as some popular culture mythology would have it. Even in the 6th century Codex Justinian, which was heavily theocratic, Paganism wasn't outright outlawed, rather certain pagan practices were. Indeed it appears that the church was more concerned with heterodox Christian practice, and in this case, while I can't think of any specific event of Christians fleeing to the Sasanian empire, various Jewish-Christian Gnostic sects flourished in Mesopotamia. Syriac Christians were organized under a single leader in Ctesiphon in the early 5th century at the request of the Great King, and soon broke off with the "Western" church.

But no, I don't know of any attestation of "pagan refugees".