Final convictions remain on your driving record forever. It is up to an individual insurance company, however, to determine how far back will they look at your driving record in determining your insurance rates. The key with moving violations is to do whatever you can to prevent convictions from ever being reported to the DPS.
Points affect you for 3 years, and too many points will lead to surcharges. But, the conviction will be on your driving record forever. You should try to get one deferred or do driving safety course if you haven't already taken a conviction.
I agree with my colleagues. Convictions remain on your record forever. It is advisable to hire a local traffic attorney to help you fight your speeding tickets and keep your record clean.