Beyond cultural acceptability, there is objective optimality. Since men thrive to validate themselves by providing more than they consume (cf. article again), it's a comparative disadvantage for women to raise kids without the benefit of that surplus.
In a society where it's reasonably easy to secure a (male) provider, you're a major loser as a woman if you can't secure one. In a society where it's hard, e.g. due to skewed gender demographics, it's acceptable to be a single mom.
There's been a quite politically incorrect paper about black US communities, their lack of men due to huge imprisonment rates and higher mortality, and the resulting prevalence of the single mom model. I think it was referred to by Freakonomics.
There is some counter-evidence to this claim: http://en.wikipedia.org/wiki/Dear_john_letter
"Dear John," the letter began. "I have found someone else whom I think the world of. I think the only way out is for us to get a divorce," it said. They usually began like that, those letters that told of infidelity on the part of the wives of servicemen... The men called them "Dear Johns".
Or don't get caught....
Also, while the man is out at war, the woman usually won't be procreating with anyone else until the man dies. The news of his death will probably affect her badly, and procreation is probably the last thing on her mind at least for a while (after which she may be too old).
But yes, hard data would be even better.