Obviously this is just a guess, but I had a similar fault on a car in my shop once ... In that case the intake for the fuel pump had become detached from the pump. I don't know how your pump is positioned, but most FI pumps have a screen/filter on the intake side that sits at the lowest point in the tank. If the pump and strainer became separated, you could have fuel in the tank but it would not be drawn up because the pump is sucking air as it sits slightly higher in the tank. Obviously if this is the case, the symptoms will repeat at the same fuel level every time.
If it were a venting issue you could run with a low fuel level and the cap off and be fine...
From a diagnostic point of view, I'd be looking into whether it looses spark, fuel pressure or injector pulse when it dies, or perhaps some combination, but you'd be best to let the dealer sort it out I think. If their answers seem vague then try to takle it yourself.