The uno still works fine afterward when tested with battery or tested with 0v/-28v power source without downstream device being connected. Given the system can operate only once, it makes me feel the problem is coming from somewhere after uno is charged.
Is it likely that somehow the ground is sending some unwanted noise (from the output BNC connector due to the triggering of downstream device, please see photos in reply #5) back to the power power supply and that interferes with the circuit of power supply??