Monthly fluid loss in normal driving from a properly sorted out cooling system in good shape should be negligible, so no doubt something's going on. I smell a head gasket (and/or worse), but there are several cheaper and easier things to look at.
I usually don't recommend "shotgun" replacement of parts (as opposed to diagnosis), but a radiator cap is trivially cheap and easy, and the thing has a lifetime of a few to several years so you probably need one anyway. (Amazing how much cooler an engine with an aging radiator cap starts to run when a good one is installed, even absent other physical problems with a cooling system. It's meant to run with a certain amount of pressure, and the radiator cap is one of the items tasked with holding that pressure.)
Nose around all the hoses, also, to be sure it isn't leaking out. And have a good look with a bright flashlight at the vicinity of the water pump when the engine is cold and again when hot (hands safely out of the way, of course). Soft-parts overhaul of a cooling system is not that difficult for the do-it -yourselfer nor very expensive, though perhaps where you live it isn't the season.
As others have advised, a pressure test is a good thing. I'm told that a smog tester can also be used to sniff for exhaust gases around the radiator cap.
Hoping it's something easy and cheap,
--Joe