As the statue nears the top of the path, it becomes more difficult to drop a villager on the narrow hotspot. 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.

If that doesn't work, and you bought the game directly from LDW (virtualvillagers.com or ldw.com), please look on the game's menu screen to check the version number. If it says 1.00.02 or 1.00.03, please see this post.