The important thing to remind yourself of, however cliché, is that this is not your fault, and it's not their fault either. However, what you believe is for the betterment of their condition may not suffice, but they need you. Don't try to remind them of all that they have to live for because they've been trying to do that this whole time. They've made the lists, they've run through the rationalizations, they've tried to make a choice, but the fact is, they have no choice.
The Hopeless are a damned few. They will run, and they will push, and they will break, and scream, and cry, and eventually they will go blank. If they had a good, long run of being awake, know that when the Hopeless falter, when they start to slip, the claws of comfort that is being asleep are welcoming them with open arms. They don't want to be empty. They don't want to be gone. They don't want time away from you. Remind yourself that sometimes people who are drowning can be saved by a simple pull of another's hand and a pat on the back, and others need a full searchlight, lifeboat, and resuscitation. They love you, however deep they are in their Hopelessness - use that love as the strength of your hand to hold or lifeboat to board. That's the only Hope they have.
And I want to tell you, between you and me, that these people, they do have Hope for something. They live and breathe and go on for the simple Hope of having Hope. And no, you may not be able to give it to them. It's not a gift you can wrap up in the most colorful of bows. But what I can tell you is that the absence of Hope isn't the rejection of it. They are here because they want it; that something. I am here because I want it… and that's the only Hope I have.