With what I am understanding so far: the water never rises to the bottom of the dam, water level drops to this hole, and the hole always has water.

Heres a shot in the dark......Could it be that the water in the hole is at water table level, thus staying at that level all the time. Then in that water hole could be a passge way that lets water in and also lets water out. Usually by me, if you hit that kind of situation the water either drains completely out, but more often gushes out filling the whole(thus creating a spring).

I would be tempted to try and pump that hole out with a trash pump and see how quickly it fills back in. If it does, you may have hit a spring that is also letting the water out. Then you would only have that spot to line with clay(I think)....Just a thought, worth only a penny.