By increasing amount of particles, you are increasing amount of transparency bounces needed to obtain transparent hair.
For amount of children equal 50, set transparency bounces to 24 under Light Paths panel, and there is no more problem.
For amount equal 100, you have to increase this setting again.
Problem is that more bounces you have, longer time takes render.
Particle system was done before Cycles. Particles display can be handled by textures managed the Blender Internal way.
You can bake Cycles procedural texture as an image. Then, you can re-use this image as a particle texture using UVmap and influencing Density setting.
At that moment, particles hidden by texture are also invisible in solid view and you don’t have to increase Transparency bounces for a Cycles render.