Declining oil extraction threatens to cause a massive Malthusian die-off for reasons outlined here. But it more immediately threatens cryonicists in two ways.
First of all, a decade from now the U.S. could be under some kind of military dictatorship that rations out the remaining energy supplies, and it will simply stop the production of energy-intensive nonessential commodities like liquid nitrogen.
Secondly, fuel shortages threaten cryonicists who live well away from the cryonics organizations in North America, especially cryonicists in Australia and Western Europe. The international airport in Sydney, Australia, experienced a disruption in its supply of aviation fuel some months back because of problems with the local refinery that produced it, so it was conceivable that a cryonicist who deanimated in Australia during that time would not have been able to catch a refrigerated flight to the U.S. in a timely manner. A much longer disruption in the fuel supply would have led to the cryonicist's being buried or cremated, because Australia lacks the facilities to perform and maintain cryotransport.
