The driver's manual for North Carolina does state directly how long points are kept on a motorist driving record. What it does say is that if you are convicted of certain motor vehicle violations in North Carolina, driver license points are placed against your driving record.

It goes on to state that if you accumulate seven points, you may be assigned to a Driver Improvement Clinic. The clinic fee is $50. Upon satisfactory completion of the clinic, three points are deducted from your driving record. If you accumulate as many as twelve points within a three-year period, your license may be suspended. The accumulation of eight points within three years following the reinstatement of your license can result in a second suspension.

From this information it would appear points stay for at least 3 years, while the offense may stay on your driving record longer. I would suggest contacting the NC DOT Division of Motor Vehicles directly to find out how long points and moving violation remain on your driving record.