This is a very interesting article on parenting and how there is no such thing as a "perfect parent." Particularly in Christianity, we do often place a lot of weight on parents, assuming if you're good enough of a parent, you'll have good kids, so if your kids have problems, then you suck as a parent.
As a therapist on a child inpatient psychiatric unit, I see many parents who place this judgment on themselves (and many of them are not Christians). They also ask what they can do differently.
While many parents could do significantly different things and definitely contribute to kids' issues (in fact, many kids don't have a problem--their families do), there is a significant number of situations where there is no clear answer. No one has necessarily done anything wrong. The child just has serious problems.
It seems these are some of the most difficult situations, both for the family and for me, as the therapist. If it's someone's fault, at least there's a solution and therefore hope. If no one is at fault, hope becomes much more difficult to find. And hope is critically important to life.
I'm not a determinist overall, but some things are determined. The thing is we cannot always determine what is predetermined by genetics, God, or our situation (or all three). What I can say is that even when we do everything right, everything does not always work out perfectly. And that can be more distressing than if we have made a mistake.