@Dinsdale Your screenshot shows an error that happens during pairing in the Bluetooth setup - possibly a timeout during the process. Re-connection is handled by the OS, there's no RetroPie script involved afterwards - so I don't think that's the problem.
EDIT: you can try and pair the controller manually - see https://approxeng.github.io/approxeng.input/bluetooth.html, the Pairing with Bluetoothctl section).