Ovens draw a significant amount of electricity; a faulty wire or outlet can cause a convection oven to not turn on. Problems with the igniter or gas line can lead to a lack of heating as well.
Convection ovens draw a significant amount of electricity. While electrical cords typically stay connected, it's worth pulling the unit out and making sure it's still plugged in. Cords used to power ovens are generally durable, but wires degrade over time.
Most newer gas ovens rely on an electrical ignition system. These units typically make a clicking sound when activated, so if the oven stays silent when turned on, the igniter may need to be replaced. Older systems might use a pilot light to start the combustion process; therefore, relighting it can get the unit up and running again. If a pilot light won't refire, the problem may lie within the gas line itself, which often requires expert help to repair safely.
Ovens must be able to detect their operating temperature, so a faulty thermostat can also cause an oven to shut off right after it turns on. Newer ovens also have a number of safeguards to prevent unsafe operation, so they might fail to turn on at all if the thermostat is not functioning correctly.