Not quite defiance. If you're hoping for something, there is a chance it won't happen, so the likelihood of it occurring is expressed in "odds". Odds of 2 to 1, for instance, means something is twice as likely not to happen as it is to happen. Something with odds of 100 to 1 is very unlikely to happen indeed.
The author is saying that whatever the odds, even at several thousand to one, the Afghan women are able to maintain a hope that a favourable outcome will occur.
I would add that in the face of all odds sounds very odd to me. It sounds to me like a combination of two separate idioms:
- against the odds, despite the odds, or (as the Major said) whatever the odds = despite the fact that this was or seemed unlikely to happen, and
- in the face of opposition, competition, prejudice, hostility etc = despite the effect of these factors