I would look at how he is recovering after the teeth trims. Is he taking a lot longer to bounce back? If he is just getting back to normal shortly before it's time to go back, that's not a good life. How stressed is he getting his teeth trimmed? Is he able to still be a normal chinchilla or are you having to hand feed him his meals and is unable to chew on things for weeks? Or is he unable to even resume being a normal chin, eating hay, chewing sticks, etc at all? Basically look at his quality of life, is he in pain and recovering for more time then he is normal and happy? With his age, and having to take him in so frequently I would say it's getting to be time.
Another thing to consider is how the x-rays look, teeth trimming only takes care of the crown of the tooth, the roots grow too. Are the roots growing through the jaw bone or up into the skull? Both of those situations will cause serious pain, and chins are good at hiding pain so you may not realize how much pain he is in. Once they get to that point the kindest thing to do is end his suffering, before the roots actual puncture something.