That's today's "Gatsby" sentence.
Amount/can challenge/what. That's the subject/predicate/object. The most important word is heart. The heart is modified by ghostly. It's a man's ghostly heart which is a storehouse — a storehouse invulnerable to new things. New things come in the form of the opposite of stored-up ghostliness: fire and freshness.
A ghost is the opposite of a living person. What is perceived here is the impossibility of living. (The impossibility of living once you have lived.)