It will not drop off your record automatically. And, no, it does not stay on forever, like DUI. However, in order to have it removed from your record, you need to take certain actions. The first is to complete all the terms and conditions of your sentence (fines, community service, etc.). From this point, the clock starts. You can learn more about the procedures and requirement by viewing the link on Vacation of Misdemeanor Convictions.
Aaron is right, but if your Neg 1 conviction was a plea bargain from an original DUI, you likely won't get a judge to vacate the Neg 1 until 7 years have passed (because the Neg 1 can count as a prior offense for purposes of mandatory minimum sentencing requirements on your next DUI that occurs within 7 years of the first one).