1999 Honda, missing antifreeze?

So my wife's Honda Odyssey is losing antifreeze on a fairly regular basis, something like a quart or so a month.

There's no visible leak, no huge clouds of white smoke from the exhaust, nothing in the oil. The only odd thing I've seen is that it doesn't seem to be pulling anything from the overflow tank as that remains full even if the main radiator is low.

Suggestions?