Leaves disappear in game mode

I've googled this to death, but can't find a solution. Any help will be much appreciated. The leaves I made for my trees are images on planes. Once in Unity, I tried setting the material shader to transparent and to cutout. In both instances, the leaves look fine in the viewport, but in game mode they disappear when near the tree. Obviously, this won't do. Any solutions?

Thanks!

See video here