One verse theology is always deficient. Context is everything.
Jesus has already pointed out that the men attacking Him have no interest in the message of God. He has used various expressions to convey this: they "do not believe" (John 8:46), they "do not hear" (John 8:47), "the word finds no place" in them (John 8:37), they "cannot bear to hear" the word (John 8:43). This rejection proves that these people "walk in darkness" (John 8:12). They have rejected the one and only source of spiritual truth (John 8:12), and so they will die in their sins (John 8:21) instead of finding forgiveness (John 3:36).
Jesus's words here are in contrast to those who do not "hear," "walk," or "believe" according to His message. Those who "keep His word," in this context, are those who express saving faith in God's Son (John 3:16–18). Those who reject Christ, however, are condemned to spiritual death (John 3:18; John 3:36).
You make the same mistake they did, to think he's speaking of physical death.
52 At this they exclaimed, “Now we know that you are demon-possessed! Abraham died and so did the prophets, yet you say that whoever obeys your word will never taste death. 53 Are you greater than our father Abraham? He died, and so did the prophets. Who do you think you are?”
Christians are dying all the time, just like Billy Graham, who "perished" and did not "reap everlasting life" - "The wages of sin is death . ." (Rom 6:23).
Once you move beyond the simplicity of it, it gets complicated.