We ran as low as half an inch last year without issue. We could drive and turn anywhere and never got hung up. Just because your ground clearance is less than a bump doesn't mean you'll get hung up on it. Lots of teams had less than 12 inches of ground clearance in 2010
On a "flat" field, I would recommend a half inch minimum. On a field with any obstacle, I'd probably recommend raising that up a notch or two. If next year's game has obstacles, we'll probably just throw bigger wheels onto our drivetrain to make it easy.