I don't have the booklet in front of me so if I recall correctly, it says that at the end of each round if Ahsoka is on the board we should remove her. Then there are 2 events that brings her back, basically each time a door opens (except the door leading to the computer). So I understand that Ahsoka will have no more than 3 activation for the entire mission.
Now what if the imperial player concentrates fire on her and she suffers more damage than her health points? Does she comes back whenever a mission event says "to deploy her on the black point" even though she was defeated (wounded) in a previous round?