This is an extremely tough situation. Plucking often becomes a nervous habit. I myself, as a human, have something similar. I chew on my thumbs when I'm nervous / stressed / bored. My thumb knuckles used to be red and chapped because I would constantly chew on them but now with a better job, more pay, less stress and a more balanced social life I've realized my left hand is completely healed and my right looks 100% better. I believe this is the same for birds - keep them busy.
With Jenga - my CAG - she has the issue of overpreening her feathers and it's on the verge of plucking. I won a "cage makeover" and we are going to design the cage where she no longer will be fed out of a bowl, but will have "foraging stations" throughout the cage and she will have to spend several hours a day foraging for food - I believe this will GREATLY help her with her preening problem.
It could also be diet - what is your bird eating? ZuPreem - the fruity pebbles kind for example, the dyes can sometimes cause allergic reactions that would cause birds to preen or pluck. Same with dry skin and dust, is your CAG getting regular baths / misting?
You can also try relocating their cage. It could be stress, but of the fear type. Maybe they don't feel secure where they are now. Try moving the cage to another view, room or against a different wall and see if that helps.
Good luck!
Hopefully someone experienced will come along with advice soon.
