Actually ignore the disengagement part it takes us down a blind alley,
its more about the intervening contests being able to insert
themselves between the PCs and the big bad, and even this could be
satisfactory decided based on outcomes in the main contest.
i.e. you roll badly and suffer a major defeat in the chase and as a
side consequence the big bad manages to put an obstacle between you
and your quarry, defeat that in order to continue with the chase.