If you are losing oil, there are only a few possibilities:
1) Engine Leak: Check all over the engine. Certain model years had a nasty habit of leaking from the rear passenger side head. There is a new head gasket that Ford uses to correct this problem.
Look at oil filter, drain plug, front/rear main seals, etc.
Note: I often degunk/steam clean my engine so I can see issues like leaks happening. All too often I look at engines, and they are simply a MESS, so much so that an oil leak would simply go unnoticed.
2) Burning: Rings may be bad, but you can check compression to determine this. Also, if your valves are not seating well, this could happen, but again, a compression test will determine this.
Also, you will see blue smoke from the exhuast if you burn enough, and smelling real bad as well.
3) Leak into coolant system: Another type of head gasket leak can have oil going into the coolant system. Usually you can see this as an oil residue in your expansion tank. You can also have coolant in your oil system if this happens, and this would be seen as a milky substance in the oil you drain.
If what you are telling us is: No leaks have been found, no milky substance in the oil you have drained, etc. then I would get a compression tester and check out those rings/valves.