Running out of oil between oil changes

Ford's rule of thumb was one quart of oil consumed for every 900 miles was deemed acceptable. Now, they say one quart every 1,500 miles is the rule of thumb for the newer engines. Sounds like you are consuming more than that. A leak that big externally would leave puddles somewhere. Sure - an inspection for leaks is a good idea anyway, but I suspect your piston rings are allowing oil consumption. This is somewhat common for Ford's "modular engine" designs starting in 1991 until recently. Common, that is, if oil changes have not been occurring religiously since new at 3,000 - 5,000 mile intervals, using 5W20 oil - high quality - and a high grade of oil filter (such as the original equipment Motorcraft). These engines are very sensitive to oil change frequency. That said - it appears to be too late for any reasonable repair process if you in fact have no visible leaks. At some point, an engine replacement is in order. Good luck.