[Arwen Imladris]

I don't think that Frodo is being selfish. He is carrying an incredible burden. To complete the task, he has to have hope that he will be able to perform it. He knows that the ring is overcoming him. He needs to know that once the ring is gone, he still has a chance at being alright. He sees Gollum as himself in the near future.

Although I'll admit, 'need' is a very strong word, I think that Frodo honestly believes that he needs to have hope. Who doesn't need to have some hope? Very few people are content with the way things are at the moment, but the happiest people are those who have hope for a better future. So, perhaps Frodo could have continued to breath if he had no hope, I don't think that he would have been capable of completing his task.

After Gollum died, he lost that sense of hope. He felt that he was doomed. And indeed, he did not ever really 'come back'. He stayed in Middle Earth just long enough to set his affairs in order and to say goodbye to his beloved land.