Hindenburg's death was pretty much perfectly timed for the Nazis and for Hitler's ambitions at creating a unitary structure with him at the undisputed head (the position of Führer). I know he was an old, old man and not in the best health, but stranger things have happened than people living to their mid-90s.
If he were to do so, and retain some degree of sanity (he appears to not have been a senile wreck when he died, he was just old in the body), what happens for the Nazis? Assume he lives until the next Presidential election, which would be in 1939.
So, what happens? Do the Nazis simply bump him off or talk him into retirement? If they don't, what does the continuing lifespan of a German national hero in the Presidency mean for the centralisation of power around Hitler?