I thought that the definition of the Lagrange point was that it required no energy to remain in that position. Or does that happen because the Earth and the moon wobble a bit and therefore the exact position of the Lagrange point shifts?
I don't know much about Lagrange points specifically, but it sounds like this one is an "unstable equilibrium". Even if you could park on exactly the right point, any tiny force (changing gravitational pull of other planets, dust impact, even light pressure from the sun eventually) would nudge you off of it and you would start accelerating away from it.
L4 and L5 are stable (see Jupiter's asteroid collection), but the others involve essentially trying to balance on a infinitesimal pinpoint, with any perturbation causing one to "fall off" and move away.
