Ship of theseus is solved by the VIN plate. That plate is the car, and moving it across chassis is illegal. It's not easily damaged accidentally, and it also can't be easily faked.
I trust that you believe that you have answered the question. My question is, to clarify, which part of the robot will you not be able to replace under pain of death?
Anything that the manufacturer and/or government regulations designate as the main body. Data plate above the door 1 Left, VIN plate under the front windscreen, engine room firewall, metal plate embedded around the magazine well left side, framed certificate hanging on the wall, a consecrated amulet placed somewhere in the lower deck, doesn't matter. Everything else are parts, which can be separately defined and controlled as dangerous items if need be. Generally that works.