I've got an answer for the guy below me, because I had the same issue.
What goes rwong in the sniper can't shoot situation, is that even though there are people and there is ammo, the tower needs an X ammount of wood to become operational. If you place the tower, put 11 people in it and like 50 ammo, you're occupying allot of people and it takes longer for them to supply the wood needed to get it operational. I personally place 50 ammo and 1 to 6 people in it and wait for the survivors to supply the wood, and if needed, then I put the maximum of 11 people in the tower.