I've not used the Audiobox 96, but other interfaces like Focusrite Scarlett. Same problem as yours.
The only way I got it to work is with an USB hub between the lightning->usb adapter/camera connection kit and the interface. It has worked with powered and sometimes even un-powered hubs on different apple devices.
I don't think the power supply that goes to the adapter increases the limit of current the iPad is "willing" to provide to the connected interface.
Hpoe that you find a solution!