Need help with Painted Conures plucking

by Ky
(Canada)

I work at a pet store where I care for the birds that we raise and sell. I am definitely not a beginner but nor am I an expert.
Recently a friend of mine had a family member pass away. The family member had been a conure breeder so my friend had asked me to come and identify the birds and help her try to find new homes for them. Unfortunately her family member had passed away quite some time ago and since then the family and other friends had been trying to take care of the birds. Most birds were perfectly healthy and promptly found new homes. Unfortunately, there was a pair of painted conures that was terribly ill and almost completely bald from plucking. I told her the birds needed immediate care and attention, so she gave them to me.
I've had them for about 2 or 3 months now and they are both eating very well and have put some weight back on. They are very comical and verbal with me, and even try to get my attention. My issue with them is this: I just can't get them to stop plucking. The male loves my attention and enjoys coming out of the cage occasionally to watch t.v with me, but I'm always so afraid that he will get hurt. Both birds (and I don't know if they do it to each other or to themselves) pull out their flight feathers. Neither of them can fly at all! They never bleed from it, but it's still very upsetting when I notice their feathers all over the bottom of the cage. I don't know if I should try to separate them, since they're both over 5 years and I believe have always been together, but I'm afraid they're biting each others feathers.
They have tons of toys and definitely get a lot of attention from myself and my spouse, so I don't believe they are bored. Anything that I've read about painted conures mentions they are prone to plucking but are generally easy to tame, but I'm too afraid to stress them further with training, and then they seriously hurt themselves.
Does any one have any advice for me? I really enjoy the both of them, but I can't stand the painful slight of them when they pluck.