It depends on the agreement for child support that was made. Some support the child through high school or age 18 only. Otherwise, the parents have a choice as to the level of support they will provide.
That will depend on the laws in your state. It can also depend on the specific court order. Most provide for support as long as the child is a full time student.Added: Actually while the above answer...
If a custodial parent receives child support for the benefit of a minor child, and that minor child has a child themselves, they can receive child support for their child, however, as far as federal...