A bit of caution here: The Second Amendment doesn't mention felons or the mentally ill, only "the people." It has fallen to other authorities to restrict those groups. Because we have allowed those "authorities" to do so, we have paved the way for them to restrict certain types of firearms from the general public. In essence, we traded our freedom for a bit of perceived security.
In fact, the Constitution does mention felons, albeit indirectly - the Constitution provides that a person may not be deprived of life, liberty, or property without due process of law.
"Liberty" encompasses the right to arms.
Just as imprisonment is a punishment for a crime levied upon conviction by a jury persuaded beyond a reasonable doubt of your guilt, so is loss of your right to arms.
Likewise, someone insane would need to be deemed so by due process of law in order to be denied liberties.
If someone suggests that the Second Amendment applies to prisoners, you can tell they're not being intellectually honest about it and are simply grinding an anti-gun axe.