They told the story about having their first baby when they were very young and newly married, and they then practiced some sort of family planning or birth control and she became pregnant anyway, which resulted in either a miscarriage or stillbirth, I don't remember which. They were devastated and prayed and prayed for guidance and made a promise to God that they would accept, love and raise any child that God chose to bless them with. It would certainly appear that they have lived up to that promise.
It was a very touching story and, while I don't presume to speak for the Duggars at all, it very well might explain why they don't practice any form of planning other than God's will. Who are we to judge?