Apocalyptic Logistics: Enabled, to some degree, by the way in which the Imperial Emergency Management Authority is staffed by ever Crazy Prepared-type that the Imperial Service has available. (Manufacturing is made somewhat easier by cornucopias, but they too depend on central nanoslurry supplies and energy supplies, so it’s not like they’re a panacea in this department.) But the EMA is notorious for its Crisis Citadels, entire mountains and asteroids stuffed with emergency supplies of all kinds, and their smaller local counterparts, and their deployable disaster pods – and even for sponsoring the engineering of things like home-growable pharm plants. Oh, and emergency command centers build aboard giant flying-wing aircraft that never land to ensure that ground-based disasters can’t take them out. Which are themselves redundant. (In full accordance with the traditions of the Imperial governance – it may not do much, by design, but those things it does do it does very well indeed.)
As a side note, it also helps that Flamic doctrine takes its negentropy seriously, and as such the faithful are expected to be as well prepared for emergencies as, say, the Mormons, with some extra emphasis on rebuilding.
…civilization may one day fall, but the forces of entropy are going to have to work for anything much more than a stumble.