He holds on to the moments they spend together.  He watches her open up and then shut down.  Her inconsistency makes him want her even more.  Something about her attention makes him feel super human, so he savors whatever she is willing to give.  Deep down, he knows that she will never be his.  So for as long as he can, he has decided to be where she needs him to be.  It’s just a duty to her that he can't explain.