Stability cant be achieved in a nuclear war always remember not only BTC but also our all the technology, development, progress, and evolution cant stand against nuclear war as much I know remember the famous words, I don't know Which type of weapons are going to be used in WW3 but in WW4 there will be Axes and Hammer of stones.
I was sure somebody was going to quote that, but that's just not going to happen.
Assuming enough population survives after this to start a new war, do you think people will suddenly forget how to craft weapons? Even if a nuclear bombardment happens in every city on this planet there will still be enough scraps, and enough raw materials for everything to start just in a few years as it was before, it's not like we will be reduced to monkeys! There are thousands of pipe guns right now in the world, guns that look like coming from a zombie game, that can be crafted from scrapyard parts but they are still lethal.
Just think, if a nuclear war happens will thousands of people forget how to melt iron, how to get coal, or how to build an engine? No!
As for Bitcoin, it's all a matter of the scale of what that war will be, and more important what surviving means.
A copy of the blockchain will survive, a few computers or hopefully a few ASICs to keep mining also, let's ignore the difficulty adjustment and others, but would that mean people will still find a use for it? Cause things like sending money in minutes on the other side of the globe from which a few nukes just came might not be a priority anymore.