It's really a curious thing how a bullet settles down to an optimum after it leaves the muzzle. The way I understand it is in part as has been said here several times already...diminishing overturning moment due to velocity decay.
That's only a part of the story, though. That overturning moment is "frustrated" by the fact that gyroscopic precession always forces the bullet to react by moving 90 degrees in relation to the direction the aerodynamic force would cause it to move (that is what causes the coning motion). It's like a cat chasing its tail. Since the aerodynamic force (overturning moment) is constantly diminishing, the coning motion diminishes also until it is essentially gone and the bullet finally takes on what Nennstiel refers to as the yaw of repose. It's fascinating stuff.
