This is only relevant if you think there's a non-trivial possibility of humanity reverting to a state where electronic transactions are not possible (or are rare), versus continuing to progress towards just about every transaction being electronic.
Considering the shear efficiency of a digital instant message, SMS, an email, or the like; all of which are protocols that can use any form of IP connection as transport infrastructure, including modems over ham radios; I consider the breakdown of bulk transportation a more likely event than the persistant breakdown of the Internet. It's become so important and so effective a form of communication, that every urban area in the world is going to have someplace in the city supported by some group of people to maintain an effective connection to the rest of the world digitally. Even if that just means that some places can only get 14.4 kbaud over a well protected ham radio setup powered by a solar array scrounged from those highway traffic displays. Even a mad max scenario still has the fiber optic cables in the ground, so nothing short of a human extinction level event is going to stop the Internet now, and in not much longer, that will include Bitcoin. Hell, there are already ham radio sats that use IP protocol. If it can run on an android phone, bitcoin can probably run on a satelite.