The small discretization and rounding errors accumulate over the time. Small deviations of the initial values can be amplified also. So the general rule is, that a longer integration time can cause larger deviations of the final value.
Of course a stable trajectory does not suffer from this: e.g. a falling pencil will be at the same position and some houres also, so increasing the time will not change anything.
This concerns the real world also: To determine the exact position of the earth in 1 million years, you need to know the current position with an extreme accuracy. But, by the way, even the "year" is not defined accurate enough for this job.
