HELP ! Losing coolant, but no leaks?

The first thought that comes to mind is that the coolant is getting pushed out the reservoir overflow tube when the engine warms up because of a bad radiator cap. A pressure test won’t show this, because one has to remove the radiator cap to do the test! You can test a radiattor cap with a thermometer, a hotplate, and a Pyrex vessel. Simply hang the cap into the water, turn the hotplate on, and see what temperature the T-stat opens at.