Unless there was some stipulation in the DUI conviction that the convictionw would be removed, a DUI conviction may stay on your record forever. You would need to contact the court records department for copies of the conviction to know more. You can certainly speak to an attorney for more information about the status of the charges.
As far as maintaining your H1B visa is concerned - an experienced attorney would probably be of great assistance to you in this regard. A fairly minor DUI conviction may not present an obstacle that can't be overcome with regard to the visa status, though the circumstances of your case may be unique. Failure to disclose required facts to the USCIS, including if you are required to disclose the conviction, would generally be problematic, however.
Have you browsed through the information in LawInfo's Free Legal Resource Center to learn more about your issue yet? See:
http://www.lawinfo.com/consumer.html. I do suggest that you contact an attorney to determine what legal options may be available for your situation. In the meantime, you may be able to learn more on your own through the LRC link I just gave you – either search the "Free Legal Resources" or browse any of the Consumer Resources on the page. Good luck.
See also:
http://www.lawinfo.com/fuseaction/Cl.../categoryid/62
http://resources.lawinfo.com/Search.html?q=h1+b+visa