Diagnosis
The convection fan is designed to cycle on and off to regulate temperature, but if it's shutting off for long periods or the oven isn't maintaining heat, it could be a faulty temperature sensor or a fan motor that's overheating and cutting out.
How to Fix It
First, ensure the oven isn't overloaded and that there's at least a few inches of clearance on all sides, especially the top and back. Poor ventilation can cause the internal electronics to overheat. Run the oven empty on convection bake at 350°F and watch the fan through the door. Note if it runs consistently or cycles off for minutes at a time.
If That Didn't Work
The issue might be with the fan motor's thermal cutoff. Unplug the oven and let it cool for several hours. If the fan works again normally for one cycle then fails, the motor is likely failing and needs replacement. You can access it by removing the back panel, but it's a more involved repair.
Heads Up
A fan that isn't running turns your convection oven into a standard (and inefficient) oven. Your cooking times will be way off and food won't brown evenly. If the fan is consistently unreliable, stop using the convection functions until it's fixed to avoid ruining meals.