As the others replied a blown head gasket would be one of the more expensive possibilities.
However, there are several other possibilities.
First off IIRC (and its in the owner's manual) the original coolant was Honda long life Type II. If somebody's changed it to something different (unless its an improved Honda replacement for) then make them change it back.
Incorrectly purging the air from the cooling system will eventually cause it to burp it out the overflow jug. A couple of jug refills is about right. But it should have happened within a couple of weeks of the service. Been checking the coolant that frequently
Any small leak(s) will easily evaporate and not leave an easily locatable trace. Pin holes in hoses or radiators are not uncommon. Pressure testing the system will reveal such leaks. And can also be used to diagnose a blown head gasket if _carefully_ interpreted.
A failing or damaged radiator cap can cause coolant loss. I'll save you the read (and my fingers the wear) of all the "technical" details. You'd need someone in the know to quickly and easily inspect the cap for these type problems. Also any damage to the mating surfaces for the cap inside the radiator can cause the same thing.
A leak in the overflow jug itself is also easy to overlook. Cracks or pin holes that would cause a slow, small steady loss.
Damage or restriction to the overflow jug's _hose_ can cause this too. Look carefully.
that's about it, short of something much worse or obscure that is so rare its not worth mentioning. A pressure test after all the basic inspections needs to take most of a day (test with the engine cold then hot and leave it under pressure between a couple of re inspections) should reveal the source if none of the above are found to be the culprit.
Please let the group know the ultimate outcome (in this thread). Your good "record" of this extra effort has also motivated me for this reply.