These are meta-stable, in that only a perfect initial state (positions and velocities) will be stable. Even then, I expect quantum uncertainties would kick in at some point. (In the simulator, the default system goes unstable at about 500 seconds, probably due to the limits of floating point math.)
>probably due to the limits of floating point math
It's due to the integration scheme (2nd order, albeit symplectic) and time step (5e-4, ok if better scheme is used).