Get with the program, this is a doomsday scenario. There _are_ no more governments. People will be doing hashes by hand.
LOL, seriously, whatever even causes a loss of a "stable internet infrastructure" for an extended period of time is probably the type of event that makes me not give a crap about bitcoins, but rather, how to find food.
I think that's where a lot of people who think about doomsday scenarios - particularly goldbugs, in my experience - have it completely wrong. Absent some sort of order to protect your wealth, wealth is meaningless. The only thing that's of any worth in a doomsday scenario is power, and it's a pretty flimsy assumption to think that the "wealth buys power" thing will carry on past the era of governments.
Having gold, silver, or Bitcoins is basically every bit as useless as having government dollars in a complete, no-turning-back doomsday scenario. They make excellent hedges (assuming you can secure them adequately and redeem them on the other side) against the fall of a government (or more than one), but if a full breakdown of society happens, all the gold in the world ain't worth shit.
Guns, land, being healthy, and having ingenuity to come up with solutions to problems are all infinitely more valuable in a complete breakdown of society scenario.
So basically this entire discussion is just silly - for Bitcoin to have any future use at all it must be assumed that there's at least some semblance of a working network - even if it's fractured, really all you have to do is make sure that restoring the links between the fractured pieces beats anyone who might want to travel from one fractured network to another and spend in both of them. Any scenario worse than that, and storing "wealth" is the least of your concerns.