Dance of the Planets was one of the best programs for orbits, and they could not predict Pluto's position a century from now, if I remember correctly. This depends on the required accuracy, of course. They had orbits for all known moons, but could not give current positions for about half of the moons. Asteroids also have very chaotic orbits because of their proximity to Jupiter. Don't expect to predict asteroid positions accurately enough to identify them in a telescope if you don't have recent orbital elements.
Some orbits are very stable and others change significantly.
I do not have any references here at work, and would have to research the topic. As it stands, you can take my comment as anecdotal.