My ex-husband and I were divorced in North Carolina in 2005. At that time, your firm helped me with our separation agreement which we subsequently had notarized but which was not filed with the court.

Neither of the parents,nor the children, have lived in North Carolina since 2007 and we have no significant ties to the state. Is there any circumstance by which the court of North Carolina would claim jurisdiction over our case?

There is a paragraph in our agreement which reads:
Situs. This Agreement, and the rights and duties of the parties hereunder, shall be construed in accordance with, and governed by, the laws of the State of North Carolina.

If you are speaking about child custody, the UCCJEA would dictate where the home state of the minor children is. For other breach issues, you could enforce the contract elsewhere, but NC law would govern the validity and interpretation. You can read more about it in our article on Breach and Enforcement of a Separation Agreement.