From This Old House Magazine October 2013
We’re talking walkways and walls here, not polished floors and countertops, which have a hardened surface that resists staining. The only way to remove rust stains that have worked their way into a slab is to (a) etch the area with muriatic acid, or (b) cut it out with a grinder. Then you have to patch in new concrete and wait for it to blend in over time.
From a series of survival skills for homeowner.