[f5fstop]

System going off is not normal, unless air temps drop, lowering the air pressure in the tires to the calibration point.
As for dealers statement, it depends on the reason. If air temps drop 40-50 degrees in one day and tires are one or two psi below recommended pressure...yes, the system will go off until the tires warm and pressure increases.
If dealer says it is normal to go off when temps don't decrease, and air pressures are ok, then dealer is clueless.
For the dealer, they have hundreds of people this time of the year bringing their vehicle in for service due to the tire pressure system going off. So far, 98% of those claims (for all GM vehicles and I would bet it was the same for all other), are due to the air pressures in the tires being set below the recommended pressure, and the temps drop at night.
It happened to me a few weeks ago, and after adding about 3 psi to each tire on Saturday morning, it has not come one since.