Use this hose-routing configuration:
It's from pre-gen bikes and better than '08-12 new-gen models because it gives petcock its own dedicated vacuum-line not shared with any other devices. You may have insufficient vacuum to keep petcock open due to leaks or cracks in vacuum hoses & fittings. Give that a try 1st.
Then if still not working, send in to ducatiman for repairs/rebuild. Tonne of people have sent him carbs & petcocks for rebuilds and parts come back factory-fresh clean and bikes runs perfectly like brand-new off showroom floor!
