Your chameleon clamps onto the screen, and sometimes the nails will get caught in the screen. When the chameleon moves on, he'll loosen and somethimes pull the nail right out.
I have a chameleon that is prone to roaming the screen of his enclosure..
So, what I did:
I took nylon clothesline, and tied 2 1/2 ft sections down from the top all the way around the enclosure. (This is hard to describe) So, the clothesline looks like prison bars all around the cage spaced about 2 inches apart. When the chameleon is climbing, he will prefer the hanging clothesline to the side of the cage and will stop clamping on to the screening.
This will solve the missing toenails, but you now have another maintenance issue. You have to replace your rope when it becomes soiled and/or becomes discolored (The nylon rope will trap water and breed bacteria)
I simply prepare "extra" rope setups, and clip them in there when I do a cage cleaning.
*note: I don't have this setup on all of my cages. With most chameleons, they will stay within the plants if your enclosure is well planted.
**note: You can also use larger spaced screening to stop nails from being pulled. Free roaming feeders will easily escape through larger screening.