I think there's two different meanings here.
1. Two people are in a relationship, whether a romantic one or a friendly one or whatever. They're trying to stick together but it's too late, it's too slow, there's nothing left. They want so badly to keep trying and going at it, but they're out of ways to make it better. Words don't work anymore, and the spark's just gone.
2. Death, or illness. When someone you love is sinking away. You keep asking them to say something, to wake up, to stay. But as time goes on, their face is slowly taken from you and your memory. You forget how they smelled and how they felt. You forget their voice, and eventually you forget everything but their name. Your memories are just memories, and there's no more laughter, they cease to exist. The graffiti artist Banksy once said through one of his pieces, “I mean, they say you die twice. One time when you stop breathing and a second time, a bit later on, when somebody says your name for the last time.” That's the end, when nothing's left of the person except what you can dredge up by thinking really, really hard.