I don't really think there is an age limit. If they think you have some hope as a littler kid, then they might put them into major therapy or something like that before admitting them into an insane asylum.
Age doesn't have anything to do with it. If you live in the US, there aren't any insane asylums anymore. There are short-term rehab facilities for people with substance abuse issues, and there are short-term psych departments in some hospitals, where patients can stay for a few days while they receive anti-psychotic medication, but there are no long-term facilities that care for people who are mentally ill. That's part of the reason why you see so many mentally ill people on the streets of every city in the US-there's no place for them to go, and no system to keep them safe. It's a tragedy, and it's shameful. But why are you asking? Do you need help?