Unfortunately, I've lost any confidence that he will finish the story.
In a span of 17 years, Tolkien wrote the entirety of The Lord of the Rings, writing his early drafts by hand, during a world war and paper rationing, all while raising his kids and fulfilling his duties as a professor.
Martin, in the age of computers, and living off his HBO royalties can't finish one book in almost the same length of time.