The ending is somewhat ambiguous, but I don't think he died at the end?
I think that Yuuko's words at the end: "let's go to heaven together," is a promise between them. She is going to continue haunting him as he is her final regret until he dies so they can finally be together.
It's bittersweet as Yuuko will have to wait even longer for him, but... she can always watch over him and interact with him. ^^
Wait!? How did he die!? And don't like the short hair who can see her she's annoying getting in the way of there love (╬ ̄皿 ̄)凸