What are the reasons for an adoption agency refusing to give a child to a couple?

Out of the 3 people that I know who have tried to adopt a child, 1 was given a child in a matter of months, 1 was given a child after 2 years (it was discovered that the social worker had previously given a child to an abusive family and was being over-cautious in this case) and 1 was refused. What were the possible reasons for the refusal?