Insurance points, and other variables that are used by insurance companies to decide on your premium rates, vary by each different insurance company. They each have their own rules and guidelines concerning how insurance points play into the whole equation.
In many cases the impact of older insurance points lessens over time. If your company adds insurance points for various traffic violations and accident claims, as time goes by and you receive no new violations and file no more claims it will appear that you are a safer driver and these insurance points could be reduced.
States have insurance law and regulations that govern premium surcharges due to accidents or convictions. For instance in New York their law allows surcharges for a certain amount of time only, typically three years. NYS also has a point and insurance reduction program that driver's can take part in to lower their insurance premiums by 10 percent.
To find out how your insurance company specifically deals with insurance points contact your insurance agent. Also they must file their rating information with your state's insurance regulatory body.