Great music lol.

Yes the reason that is happening is you have created a motion path with 30 steps (1-30) so any end value above 30 in the create motion path snap shot will have no effect.

You have to delete history and rerun the attach to motion path and increase the number of steps. You have to keep repeating this until you get the link moving the correct distance each frame. It takes a bit of trial and error.

Also I noticed that the link is accelerating at the start and decelerating at the end. To fix this remember to go into the graph editor after creating the motion path and set start and end tangents to linear.