Is it normal for a c-section scar to feel numb a year after the birth of the baby?

Can be: When the incision is made, the small nerves in the skin surface are cut. The sensation in the area may never be exactly the same.

Yes: Dr grootwassink is correct. You may find that seeing a chinese medicine practitioner and using herbs/acupressure/acupuncture can help improve the numbness and help restore the superficial nerve connections.