The P0455 code points to a problem with your car’s fuel system. Specifically, the code means that there’s a failure in the EVAP (evaporative canister) system. You may wonder if this problem will have some sort of impact on your ‘Stang’s tranny and the answer is quite certainly no. However, if you look at the sensors that are monitored by your Mustang’s engine control module (ECM), also known at the car’s main computer, you may notice that there are a couple of the sensors used to monitor your car’s engine and emissions subsystems, both.
The first is the Mass Airflow Sensor of MAF. The MAF sensor senses changes in the amount of air being drawn into your Mustang’s engine. Several systems, including the ignition and transmission, react to changes reported by the MAF. The same is true of the MAP or Manifold Air Pressure sensor (some call it the barometric sensor) which measures the pressure in the manifold and changes it according to the engine’s needs. And, then, there’s the Throttle Position Sensor which looks where the throttle is positioned and then makes the engine react accordingly, after it has reported things to the ECC.
Given the P0455 EVAP code, it is possible that your Mustang is suffering from a problem anywhere from the torque converter right through to the output shaft, however, I honestly doubt it. I would have your mechanic concentrate on the most obvious areas impacted by the EVAP system, looking really closely at the fuel-line filter for fouling. If the fuel-line filter is clogged then your Mustang would react in the manner you describe.
I would also have your tech, while under the hood, look at the gas tank, to be sure there’s no junk fouling the fuel pump. Debris in the bottom of the tank might do this. I would also have your current load of gasoline drained out and replaced with a new load. The reason is that gasoline, since it now has a bit of alcohol or methanol included for performance enhancement, can become water-attractive. Water is not helpful for ignition at all.