Gas oven never reheats
The problem was that the igniter was getting old and (presumably) failed to work under high temperature. So it ignited the gas when the oven was cold, but failed to re-ignite the gas to maintain the temperature once the oven had preheated.

The repair man said that a failed igniter often causes my problem. He was unable to explain why the igniter works by heating up and yet fails to work when hot. In addition, the the igniter is made of carborundum, so its electrical resistance decreases as the temperature increases (the opposite of metal). But replacing the igniter did fix the oven.