Thickening Alfredo sauce

My girlfriend and I are huge fettuccine alfredo fans, so we have been trying to recreate one of our favorite Italian dishes at home. The trouble we keep having is thickening the Alfredo sauce without destroying the flavor. We've tried tons of recipes (this one for example: http://ift.tt/1Ja8JFi) but the trouble we keep having is keeping it thick without destroying the flavor. When we are finished with a recipe and remove the sauce from heat, it never seems to thicken up. It just stays a kindof milky consistency and gets cold ):