In Shelley's Frankenstein, two motivations are present that keep the monster wanting to live.
First, he hopes for a female mate. He believes this will make his life bearable. He will have someone as a companion that will not be appalled by him, since she will look something like him.
Second, once Victor impulsively destroys what he has created of the female, revenge is the monster's motivation. He plays cat and mouse games with Victor, leading him on and humiliating him once in awhile just for fun.
First, then, hope for companionship keeps him going, and then revenge takes the place of hope.