In our culture people who “give up” anything but drugs, are considered losers. Why is that? The logic is as follows:
 You conscientiously choose a task, and because we consider you a rational being, the task is to achieve a certain purpose;
 You work hard on the task, and it goes more or less well;
 You succeed, and go back to  to choose your next task;
 You fail, but you don’t “give up”: The whole universe will conspire and let you re-interpret your purpose.
What is left out is the possibility of a task becoming increasingly less worthwhile as it is being performed, a certain feedback-loop between our efforts and the value of the purpose we are pursuing.
What if we feel that the value of our purpose changes? Should we doggedly pursue it, everything to prevent “giving up” and being labeled a loser? Or should we expand our idea of tenacity (or however you would like to call an “ultimate” virtue that guides us in ALL circumstances, and hence is always one step ahead of us) and consider “giving up”, under specific circumstances, a virtue?
Maybe we hold on to our purposes because we’re afraid they can’t survive on their own. Maybe we live in times of small purposes, like winning medals, making a career, or getting our kids through college? Where are the Big Purposes, the existential ones, the purposes that put soldiers in the trenches in 1914? The purposes that kept people waiting half a century for a lover, or a vengeance?
Maybe we stigmatize those who give up because we are afraid that whatever purpose it is they “gave up” can’t stand on its own.