I need three strong arguments to support the theme of isolation in The Road to be the reason for death of the father.
The Road is a dark novel of a post-apocalyptic world and isolation is everywhere. While we do not know the ultimate cause of the sickness of the father, we can safely make the case that isolation was part of his ailment and led to his eventual death. Let me give you a few points to support this.
First, all people agree that humans are meant to live in community. Aristotle stated famously that we are political animals. What he meant by this is that we all should live in a polis, which in English means city. Community is the point. If you think of the novel, The Road, the only people who live in communities are the roving band of cannibals. Based on this point, you can argue that they survive, because of their demented community. Ironically, the community of two (true community) is not strong enough to save the father.
Second, on a physical level, there was no medical attention and auxiliary help. They were alone and this fact alone created great challenges for survival.
Third, there is a harrowing alienation of everything, a feeling that isolation will turn to nothingness. This sheer sadness has a toll on the father and this may add to his death. Listen this quote: "The last instance of a thing takes the class with it. Turns out the light and is gone." How can this profound sadness, which wipes away a class or category, not lead to the dehumanization and death of people?
In short, in view of the lack of community and civilization and the the thought of the brink of humanity ceasing to exist, the real question is how the father lived so long.