There are a lot of people who can't take the Pill for various health reasons. And then there are a lot of women who don't take it because they're against it for religious reasons.
If this was mental illness, my feeling is that it is more likely to have been post-partum psychosis, which is a rare but extreme variant of post-partum depression that features not just depression, but also hallucinations and violent episodes.
That's what Andrea Yates had, anyway.
"Six babies" implies that this woman had a lot of children in quick succession, which also heightens the chances of having mental illness triggers relating to the constant hormonal upheavals of subsequent pregnancies.