No adoptive parent envisions a divorce, but divorces do happen in adopted families.
A divorce has no effect on an adoption that is finalized. However, a divorce can and often does affect the status of a foster care placement. Once adopted, a child is legally the child of the adoptive parents, just as if he or she had been born to them. If the adoption is not final, the court decides if one or both parents should finalize the placement as the marriage dissolves. The recommendation of the adoption agency is an important factor in the decision; a parent who wishes to adopt as a single parent should make sure the agency knows this.
There is no evidence to support the idea that adoptive parents are more likely to divorce, and in fact, there is reason to believe that the opposite is true. Adoptive parents undergo a great deal of scrutiny individually and as a couple during the home study process. If a marriage is on shaky ground, the agency recommends against adoption. Moreover, many, if not most, adoptive and many foster parents have experienced infertility and struggled emotionally and financially to become parents. If the marriage survives infertility, it seems logical that the adoptive parents will work very hard to keep the marriage and the family intact.
A divorce has no effect on the ability of a person to adopt again.
Single parents, and people who have been married more than once are not denied the chance to adopt again for those reasons alone. As long as the agency feels an individual can be a good parent, divorces are not a major factor. However, some countries prohibit international adoption by any single or divorced or re-married persons.