Coolant needs to be topped up every few days

Most likely suspect is a leaking head gasket. There's two ways to verify that. If coolant is being drawn into the combustion chamber, usually combustion gases will get pushed into the cooling system too. Your mechanic can do a test at the radiator with a glass cylinder with two chambers partially-filled with a special dark blue liquid. If the liquid turns bright yellow when he draws air through it from the radiator, that indicates a leaking head gasket.

You can also add a small bottle of dark purple dye to the coolant. After the level drops in the reservoir, you search with a black light, including at the tail pipe. The dye will show up as a bright yellow stain.