I had missed the post from Patriot1 and frances.
It is my fault not to clarify what I and meant. I posted this point of view in another thread, and I should not assume that everyone follows all the threads here.
Ennis will never love anybody else the way he loved Jack (if we take the "I swear" to mean eternal fidelity, as Jake Gyllenhaal has implied in one of his interviews). Here, the door to this is forever closed. But as I had said in the other post, a closed door is an invitiation for the pilgrim to enter roads not explored, and in this sense, Ennis is alive.
Judging from the tenor of how the older Ennis is described in the first dream sequence of the short story, I doubt that Ennis opens up that much in later life. He continues to dream of Jack. He remains alone, although the choice is there to live for a short time with his daughter. His daughter's love he will have; a love like that between him and Jack: never again. In that sense, he is indeed dead.