The statue of limitations for criminal activities regulates the time from the alleged crime until you get charged for it. So if you haven't been charged for the crime in X years, (depending on the crime and circumstances) then they are barred from prosecuting you.
But in your case, you have already received your tickets (charges) for the trafic violation, which may be a infraction or misdemeanor. And as cyjeff said,
They won't ever just go away.