Polygon limitations on screen

[Lima]

I have this terrain with some planes scattered on it. About 2000 planes. when the camera faces many of them, the terrain and my player model stop being rendered. I have to make the camera look at where they aren't in order to be able to see the terrain and the player model again. Any tips?
Also, the planes were cloned using the cloneObject() method. I don't really know what to do now.

few planes on camera:
https://imgur.com/k3PNGug

many planes on camera:
https://imgur.com/T18Kh3r

update:
It seems to be a limit of objects on screen; when I move the camera some planes disappear e others appear, for some reason my player model and the terrain are not a priority and are ignored when there are many planes on screen. I removed some of the copies and this no longer happens. But I still would like to place many of them around my map.

[EgonOlsen]

There is a setting for max. objects (it's called differently for historic reasons though): https://www.jpct.net/jpct-ae/doc/com/threed/jpct/Config.html#maxPolysVisible

[Lima]

Thank you!! You're a lifesaver! I had set the far clipping plane very close and removed some of the objects to "kind of" solve this, but for my purposes is not ideal, I really needed to put more things in scene.

p.s.: Again! Can't forgive myself for not seeing that in the documentation.