Unlike other currencies, the guarantee of bitcoin is that of people who own bitcoin. What happens to bitcoin in the event of a war?
When we say war, then it could be small or as big as world war. In the broad sense every country is powerful in terms of their military division and they all can make big destructions.
So, if that happens then first thing that will be attacked is internet, I believe internet will be long gone because every country knows their stuff works on that thing and to make them weak everyone will attack the internet stations, anything that links the military with distant communication.
I am sure common people like you and me will have no other way to survive but just get into war or may be stay in the basement so that no bomb hits us! Im sure bitcoin won't help us at all in this regard.
We will never know until what time the war will stay it could be months to deadly years!! Bitcoin is digital, there won't be any miners, there won't be any way to confirm it, work with it in that situation. So may be it will go down.