Seeing as how warnings are basically the non-binding resolutions of the criminal justice system, I'd say that the agency has no requirement to keep them or destroy them at any set time. More than likely it will stay on your record for a few years, maybe 7. Might be permanent. You can call them up and ask.
One interesting thing to do is to request a record of all contacts you've had with the state patrol/sheriff's office/local police/etc. They're obligated to turn over just about everything they have on you, and you can do it anonymously. You can do it in person, through the mail, or over the phone. It'll show all your car accidents, things you reported, and things you were suspected of or arrested for. It's public record, anytime someone does a legitimate background check, it's one of the things that gets pulled.