Do you want to hear the correct answer? No energy is being lost; as a matter of fact, the moon is gaining orbital energy. It does this because of tidal pumping by the Earth's oceans sloshing back and forth. The energy ultimately comes from the rotation of the Earth, which slows down slightly. The total energy (and angular momentum) is conserved.
A pendulum won't gain or lose energy by this process. In the first place, the motion of the pendulum is not phase-locked to the motion of the ocean, as it is in the moon's case. In the second place, the tidal force over the swing of the pendulum is extremely small, while it is large for the moon.
Gravity is a conservative force. If the oceans didn't slop about, the moon would stay in its orbit for all eternity. In the absence of friction, a pendulum will swing with the same energy--meaning, to the same height--forever. (A vacuum will take away most of the friction; a magnetic bearing will take away the rest.)