A faulty ignition switch first comes to mind because you are able to start it and that completes the circuits. But upon shut off the circuit needs to be made incomplete at the ignition switch. I need to refer to the wire diagram to see what relays (if any) are in the circuit for shutting down. Also a bad ground in the circuit may be the issue. Recheck all your connectoins and grounds.
I doubt that the MAF is the issue because if that was faulty the car probably wouldn't start.
Was the engine able to be shut off before you rebuilt it?