Did she have an epidural?
Some studies show that having an epidural can increase c-section rates, and reduce a womans chance of being able to breastfeed by 75%.
If you talk to women that had an epidural and tried to breastfeed, a lot of them will say "the baby did not latch on", or something like "I was not producing enough milk."
It was a complicated situation. Our son had no issues with latch or suction power. My wife went about 7 hours into labor before getting an epidural but there was already issues with heart rate. They attached an internal heart rate monitor at about 4 hours. The epidural was almost dual purpose, she was in pain and stalled at about 5cm. Combined with heart rate issues of the baby, we went ahead with the epidural.
Let me say, it was an EPIC BORK by the anesthesiologist putting it in. They placed it in and she could still feel on one side. After about 30 minutes, they pulled it back out and redid it. This time, she had hot spots. The doctor really didn't believe her.
Ended up with an emergency c-section. They realized she could damn well feel in certain areas when she almost jumped off the table when cutting her open. At that point, they just pumped her full of morphine and finished up. It didn't take too long before she broke out in hives.
We still believe the root cause of the lack of milk was the antihistamines because if you are breastfeeding you should avoid those anyways because they will cause a drop in milk supply. In this case, she just never got started.
That all combined with other factors, my son ended up being jaundice. We had to take a billy blanket home with us and get him tested every other day for the first week. The jaundice was another primary driver in supplementation during the first month until she got a supply going.
EDIT: And the reason for the heart rate drop. He did have the cord around his neck. They attempted to float it out about 3 times during the labor but were unsuccessful