One way that vacuum causes bad fuel mileage: engine vacuum is used to control a lot of little valves under the hood of your car. PCV, ICV, EGR, Trottlebody stuff, fuel pressure regulator, power brake booster, etc. Heck, even the flaps in your AC vents that dictate whether the air blows on your feet, face, or windsheild are vacuum driven! Every leak removes some pressure and causes those valves to respond more slowly. Once that happens, fuel mixtures start to get effected, because the valves are not operating at peak perfomrance.