Radiator losing coolant

With no other clues or observations to go on, the best suspect is a leaking cylinder head gasket. Your mechanic can perform a chemical test at the radiator to verify that. You can also add a small bottle of dark purple dye, then search a day or two later with a black light. The dye will show up as a bright yellow stain that you can follow back to the source. If a head gasket is leaking, you'll find the dye inside the tail pipe.

Auto parts stores have the dye, and those that rent or borrow tools should have a black light.