It could be that the leaves are flipping rather than disappearing. You might check to see if all of your paths contain a "vector orientation direction modifier". If one of the paths does not, It could cause sudden flipping. For this tree it looks like all layers should have a vector orientation direction modifier in the "y" direction at 100 Percent. This sets the up and down direction for the path, so it is pretty important. Not adding this to each path can give you unexpected results.
Random and noise modifiers can also cause flipping and mesh breakage. If you have any of these in your tree try turning them off and seeing if that fixes it. Those modifiers should be at the bottom of the modifier stack so that you don't get unexpected results when modifier commands compound.
For the mesh disappearing when < parent, you could try setting a minimum diameter. I think it overrides the "<parent" option, but I could be wrong. Real branches never have a 0 diameter, so I always set this at something like 1/16". This option is toward the top of the mesh panel.
Hope it helps!