I'm speaking under the assumption that the ABS wiring is very similar to the W-Body setup, with the wire harness traveling along the control arm to the hub.
When I ran into this same issue on my 04 Impala, I decided to just replace all of the wiring between the hub assembly and the main harness. Glad I did. The wiring I removed didn't have obvious damage, but it was extremely dry and brittle. It was as if all the plasticizer had migrated out of the wiring. If bent it would snap like a twig. Combined with the normal movement of the LCA, I could see how the wire could easily bind or break in several spots.
I believe dorman sells a piece of harness with the ABS connector and butt connectors, but I just made my own with some fresh wiring and shrink wrap. Used solder and shrink wrap to connect the wiring I cut out, and used the existing wire shielding and clips. Have had no problems since.
Hope you find my experience useful.