I had a similar problem, but with copyentity. I have a bunch of trees. If I load them all with loadmesh it works great, but if I load it once and then make all the trees with copyentity, my transparant leaves are not shown most of the time (they pop in and out of the view).
I don't know if this has anything to do with your copymesh problem though.
I don't know if this has anything to do with your copymesh problem though.