Orianna has the ability to throw her ball to allied champions to give them a shield with Command: Protect. The ball then can be used as the point of origin for her other skills.
Elise has the ability to rappel into the air and drop onto an enemy. This ability makes her untargetable by enemies but DoT effects continue to effect her. Since the shield/ball from Orianna is a buff I assume it would stay.
However, I wanted confirmation that when she landed she still had Orianna's ball on her or if it depended on the distance traveled (since the ball has to stay within a certain radius of Orianna) since Command: Protect still respects the ball leash range.
Best Answer
As long as The Ball is anchored to a champion, it is a buff, not a physical entity. This means that it'll stick around when Elise rappels, and only return to Orianna if the rappel takes her beyond the maximum range of The Ball.
The Ball, as you say, has a leash range, and Elise's movement (regardless of its relative uniqueness) does not affect this. Even when out of sight, the ball still has a position, and behaves accordingly.
It's the same scenario as when a champion recalls / uses teleport. As soon as they get far enough away from Orianna, The Ball leashes. It's not based on anything other than distance.
Finally, realize that Rappel is not some crazy-weird movement effect; Elise doesn't move when she goes up - you can see this if she dies to a DoT while in the air -- her corpse will instantly appear where she rappelled up. When she comes down, it's essentially a flash.