When fan is running- power to fan cuts in & out

That is not normal. The gas pilots need to stay burning, need pilot flame sensors too for the main gas valve in the oven to work. Who knows how the oven is set up that it all seems wrong now.
If there were a electric gas valve, the valve would be on fire and/ or seismic shut off. If fans were interlocked, it would be on fire cut off along with fire dampers.
Why would anyone control a gas valve cut off with exhaust fans? Goofy set up unless there is more to it. For now I would keep the gas on, independently from the exhaust fans, keep pilots lit and a pilot light flame sensor for oven gas valve/thermostat safety control.
Keep your oven Fromm filling with gas and suddenly igniting accidently before anyone gets hurt or there is property damage.

sounds like its not getting gas fast enough to keep burning,that happen to me and the gas line was to long of a run for enough gas keep coming. so I up the pipe runs real good the flame keeps burning, so you know you can only go 25 ft in half inch pipe then u lose your flame

It could be the flame sensor. It is located in the burner box Opposite from the ignitor. It is a metal rod with a porcelain base. The flame sensor "senses" a small electric current through the flame. If the sensor is dirty it can impede the electrical current and cause the control board to lock out. Remove the sensor and clean the rod with some steel wool or sandpaper. Reinstall and see if this solves the problem. Hope this helps.

Your Furnace is short cycling...cutting out too soon. I would call for service on this one. If it has a flame sensor and you know where it is, clean or replace the sensor. If there is a air/sail switch, make sure it is free to float/swing.

It sounds to me like your draft motor is probably shuttimg off on thermal overload. They will get to hot and shut down until the motor cools down then run again.But by that time it's caused other trouble so I think you need to replace the motor first and then see what other problems it has caused.I hope this helps you and thanks.

First, for those of you who might not know, "What is a flame sensor?" A flame sensor is a safety device. When your furnace's main burners ignite (light Up) the flame sensor picks up the heat from the furnace's main burning and says, "YES," and sends a signal back to the main furnace control board saying that it is OK to let the main burner stay on. Or if the main burners do not ignite, the flame sensor does not pick up the heat and says, "NO" to the main control board, Shut That Gas Valve and Main Burners Down! Thank God we have safety controls like the flame sensor. Most of the time, after turning your furnace's power off, you may clean the flame sensors with light sand cloth, emery cloth or steel wool. Reinstall the flame sensor and you are back in business! Over the years flame sensors can build up a light coating of burned-in dust and dirt. This insulates the flame sensor so that it doesn't sense the heat of the flame well enough, so by cleaning it you have almost restored it to its new condition. Seldom, but sometimes they do go out completely.

I cleaned the sensor that was at the the right further most burner on my Goodman and it worked. got the answer to my problem here at fixya. My burner flame only lasted 5 secs before it shut off. Thanks to all who took the time to send me a response.

Could be a dirty or faulty ignition sensor. This is the sensor that tells the heater that there is a flame burning normally. If that sensor gets dirty or fails, the heater thinks there's no flame even though there is and cuts the gas as a safety measure. Cut the power, remove the cover, and check all the wire connections to be sure the leads are clean and dry and snug. The ignition sensor is near the bottom. If that doesn't work, then the sensor might be faulty rather than dirty. Call a tech to replace it.

Tara,
If flames go on and then go right out it is usually a flame sensor problem. These are usually found on newer furnaces with electronic ignition systems. It will be located in the flames of the burner farthest away from the ignitor. If you see an orange glow before the flames light then thats it! If ignitor is on the right side then flame sensor is at the opposite end. It is a round steel probe with a white ceramic top and a wire running to it that sits in the flame and is a little bigger round than a coat hanger. Shut off power, wait to make sure it is cool to the touch, using a piece of steel wool( or sandpaper if none available) give it several good strokes to clean it. You may have to remove it from the top by removing the screw and pulling it out. I usually can clean them without removing them but I have small hands! Turn power back on and it WILL run if that was the problem!!!!!!

There are certain faults like "Flame Rollout" and "High Temp Cut-out" that will cause the fan to run continuously until corrected. If the furnace is working then some power is making it to the "G" terminal at the circuit board. Could be a jumper or miswiring.