At first I thought there is something wrong with your file or your particle system. But I recreated it from scratch with my own plane and an icosphere as instance object and got the same result:
I switched from rendering Object to Path and found the hair looked normal... but when I looked at the plane from below, some hairs were a bit more sticking out than others - and also clearly in patterns related to the faces. It's just not so obvious from above because the hair is so long.
Going back to Object I saw this was true for the icospheres as well - in parts where they were missing on the top side, they were visible from below. So I wondered what is wrong with those faces and the simple answer is, by displacing them they became non-planar and that makes the particles spawn below the surface if the deformation is too strong.
The solution, I selected all faces. Not just the ones in the group, since particles are getting spawned on adjacent faces to the group vertices too - but it would have been sufficient to select the group vertices and expand the selection by Ctrl+Numpad +. From the Mesh menu I then chose Clean Up > Split Non-Planar Faces.
I found that a Max Angle of 5° seemed to be sufficient for the most part, but to be on the safe side you can set it much lower. Of course you could simply split all of them, but maybe you want to generate as few polygons as possible.
After I did this, the particles showed up everywhere and none of them were placed below the surface. In general I think if you simply had a higher resolution on the mesh the effect would be much less visible, but the larger the faces and the higher the angle of deformation, the more obvious it becomes. Without splitting the faces, scaling the object down on the Z axis to flatten it would have helped for distributing the particles, but of course then the landscape would be too flat ;)
