So, they arrive at the classical minarchist position and fallacy because of this fear. They still want to leave, at the very least, defense up to the state. “After all,” they think, “No private firm would take up a business with the kinds of losses that war brings.” They do not think about the fact that it is for this reason that war only comes with the state. It cannot come in any degree resembling the kind of war we see today. Once the minarchist sees that his framework is inconsistent and foolish, the makes the logical jump to market anarchy.
War only poses a problem for anarcho-capitalism as long as there are foreign States. And under those conditions, it is indeed an insurmountable problem. Even if an ancap society could produce the kind of forces necessary to fight a war (it could), it still cannot fight a war without violating its own principles, as it is impossible to fight a war without either ignoring ethics altogether or making ethical judgments about collectives, rather than individuals.
But if we are theorizing about an ideal, we are free to suppose that anarcho-capitalism is global in scope, removing any concerns about war. Basically, war is a problem for the implementation of anarcho-capitalism in a world of States, but it is not a theoretical problem for anarcho-capitalism.
The real problem is dispute resolution.