Make sure the tire pressure on your 2006 Hummer H3 is correct (don't forget the spare, some manufactures include the spare) according to the tire pressure label on the drivers door pillar. Under or over inflated tires will cause the tire pressure warning light to come on. Over inflated tires will also cause a harsh ride. Oversize wheels and tires often require higher pressures, the system my need to be reprogrammed to reflect the new tire pressure requirements. If the warning continues even with the tires at the correct pressure the system has a fault which will require diagnosing.
you either have to much air in your tires or not enough air.all tires must read the same .check pressure and fix according to tire pressure approx 35 pounds each.then drive until light goes out usually only a few minutes.also they malfuntion in cold weather.if problem still exist then tpms needs replaced.
I had same issue 2yrs ago. I went to dealer and pressure was correct and gauge checked out. I notice if the outside temp went below 40 degrees the sensor would come on. Dealer stated they were aware of similar issues. Never had issues with my tires. Gauge will come on in cold weather from time to time still?