When Barbara Gordon leaves, she leaves for college. She say she needs to be gone from this life. She returns anyway. She loses her ability to walk. She returns anyway.
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Damian Wayne leaves because he feel he needs to. He leaves for the tournament on Lazarus Island. When he returns he return victorious. After that he stays.
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Duke Thomas never leaves. He needs to find his parents. They're in Gotham. So Duke stays.
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Kate Kane have been leaving her entire life. When she returns it's to stay. Her soul knows peace now or at least something she can pretend is peace.
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When Stephanie Brown leaves she doesn't get a choice. She wakes up in a country so far from her own. The day she returns are the day she swears to stay. She's never known a world outside of Gotham but that's okay. Gotham needs her after all. So she stays by the Bat's side. She may never be his but she will always be the most loyal one.
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Jason Todd didn't chose to leave. He was taken as a child. He returns as a man. He's not the same. He's ruthless, he is spiteful. He hates Bruce more than anyone else. He grows. He come to belong again. Somehow. In someway. He leaves again when Bruce dies. He returns again when Bruce does. He's never really there but he's never far away either. He never leaves again, he just doesn't stick around.
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Cassandra Cain leaves for Tokyo. She's never known family. She's not sure what to do with one, so she leaves. She comes back when they need her. She leaves when they don't. She comes back when they do. These days they always seem to need her. She can't get herself to leave again.
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Helena Wayne leaves Gotham out of need. She never returns. She can't. Her Gotham is no more. Instead she returns to this earths Gotham. This earths Bruce Wayne doesn't want her. She sticks around anyway. She becomes Bertinelli instead. She roams around a world now hers but she never leaves again. Not after what happened the last time she did.
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When Tim Drake leaves he are no longer Robin. The first one took that name from him again. Bruce isn't gone, Tim knows that. He leaves and he doesn't come back until Bruce does too. They all come back when Bruce does. Dick doesn't. He leaves again and Tim hates him for it.
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Dick Grayson always leaves. The first time he is eight and running away to find his parents killer. Batman brings him back. He keeps running away. One time when he is 11 he makes it as far as city limits. The cops drive him back. When he is 13 he grabs his team and runs all the way to the other end of the planet to save the circus that raised him to become a killer. He doesn't know. He contemplates staying. When he returns Bruce locks him in his room for a week. He doesn't leave again until the day Bruce kicks him out.
A year passes before he returns. He comes back for the sake of Jason. When he leaves again it's for space, he always planned to come back. When he does he have no brother to return to. The father that meets him are not his father. When he leaves his body is bruised. He vows never to come back again. Then Tim Drake knocks on his door and his is back in the game he's been caught in since childhood.
This time he stays. Right until the next fight and the next one and the one after that. In the end he never stops running away. He always comes back again. Jason's back and Bruce didn't tell him. This time when Dick leaves he manages six months before he's back.
He comes for Damian and then it's Cass and then Bruce is gone and he's the oldest and he's the one who have to hold it all together, he's the one who have to be Batman now. This time he's the one who stays when everyone else leaves.
Then Bruce is back and with him the others too. They blame him, they hate him. He leaves. He comes back again the next time they need him and the time after that and the time after that and every timer after that.
He will always fight with Bruce, he will always run away and he will always come back for this is the house who raised him. He wasn't meant to live his life in that godforsaken place but he did, he can never truly leave it behind. To him Wayne Manor will always be a house and not a home.