Are you sure they haven't picked up the gong piece already? If you haven't cleared away the area in front of the gong encasement, the piece won't appear (it gets stored in the research hut).

You can check by looking at the puzzle screen and see if you have that puzzle solved.

You may also have lost the gong piece by accident (if the carrying villager drops it, the piece doesn't reappear) -- you can solve this by quitting the game and restarting.

Good luck!