Part of my adoption contract with the Rab Residence says that I agree to let Caroline know if I move house so that she can re-home check and/or check accommodation again. I guess in practice it would depend on the individual circumstance. If you were leaving the bunny shed behind, potentially you could be moving them into a shoe box, but if you've got something like a happyhutch combo which you can just flatpack and move, then it's less of an issue.
I guess I wouldn't expect a re-homecheck for a good few weeks after moving so that there's time to settle everything down again, and I would hope that most rescues would recognise that.