Hi Shortcircut,
The problem is with the D+ signal, generated by the Fiat cab, which will cause the step to retract and the habitation 12V electrics to disconnect, when the engine is started. It seems that the D+ signal is not being received by the fusebox, and therefore, it does not "know" that the engine is running.
The D+ signal in your vehicle is a voltage, is taken from the alternator. If you lift the bonnet, you will see a set of relays in the center of the engine, and a blue wire come from this to the alternator. Make sure that the blue wire is firmly attached at both ends.
If that is OK, it is a case of checking the relays, and then the wiring back from the relay box to the fusebox inside the
MH. If you have one, a multi-meter may help to see read the voltage on the D+ signal cable.
I hope that helps.
Ash