There are few instances in my life where I have not played the game this way. I am not in a habit of giving up. When I detach from a task it is mostly because I have worked out what I need to put in and measured it against the rewards of succeeding.
But if the people I am working with decide to give up on me then I have even less motivation to persevere. I will not bail, but if you wish to bail out the I won't beg you to stay.
Mostly - if you don't give up on me, then I won't give up on you. I might go missing but I won't be lost forever.