As the statue nears the top of the path, it becomes more difficult to drop a villager on the narrow hotspot, and there is less room for the villagers to work. Try dropping your chief lower on the path, where the hotspot is larger. The entire length of the path is an active hotspot while the statue is being moved.
Also, check your game's version number on the menu screen. If it's earlier than v1.00.04, please see
this post.