To add to the points from others: 3+-body systems are generally chaotic, so you cannot predict arbitrarily far into the future, but the solar system is reasonably well-behaved in that manner, so the timescales are long, but we don't know where the planets in the inner solar system will be in their orbit in ~5-10 million years (as in, that's the timescale where the error bars for the position in the orbit span the whole orbit). Of course, if you care about more precise predictions then the timescales are shorter: eclipse predictions more than 1000 years in the future are likely to be quite inaccurate.
