A couple thoughts, Im no professional but that amount of water leaving an area is a big flow, I built a pond a yr or so ago and had a sink hole under it, the pond would fill up and then go back down swiftly to that one level, we wound up finding the sinkhole and were able to repair it and the pond is now full, my point is, it sounds to me like you have water going out thru the bottom to possibly a sand or gravel layer and it may be running a long ways under ground before it surfaces, if it ever does.
I dont think that it is going out thru your dam, with that volume of water you would be able to find your leak in a dam in like 10 minutes, 1 big question is how low does the water go to before stabilizes? at that elevation you will find source of your leak, theoretically, a leak of that size, running for any length of time should leave one heck of a hole. usually a big leak such as you are dealing with is much easier to find then a small nuisance leak. correcting it tho may be a different story. Good Luck!