Yes. It's kind of like the halting problem: You cannot write a general computer program that will analyze the source code of any random other computer program and tell you if it will halt.

You can write a program that will analyze the code of a few specific other programs and tell you if they will halt. You just can't do it in general.

The 3-body problem is like that. Except it's much harder to find stable 3-body problems than computer programs that are predictable.

> Except it's much harder to find stable 3-body problems than computer programs that are predictable.

Proving that statement is true might be harder than either of the other two issues.