How often would we use the expression? Never! These are song lyrics and, like poetry, don't reflect the way we speak. I guess it means that waiting has been a struggle to the point of feeling very sad, numb and lifeless.

Barbara is correct. However, I will add a little more context to the lyrics. "A Thousand Years" was written as the title song for the soundtrack of the movie "Twilight." The movie is about a vampire who falls in love with a human. In lore, vampires are essentially immortal, having lived for hundreds or thousands of years without aging. Vampires are also "living dead." Depending on the constructs of the world created in a book or movie, their hearts do not beat (or beat extremely slowly), their skin is cold, etc. So there is layered meaning to both the title ("A Thousand Years") and the lyric "I have died every day waiting for you," given the context of a vampire love story.