Sounds like a thermostat problem. It is what actually maintains temperature in your oven.
The thermocouple verifys flame is present when the gas is flowing, shuts it off when it does not detect flame/heat from burner. This keeps gas from just flowing and the subsequent boom. It can be intermittent and cause your gas appliance to shut down after working for a few minutes, but usually when they fail, they fail and with good reason they are designed to fail in such a way that the burner won't stay lit, i.e. gas is off.
In my opinion there are several scenarios that could cause your problem, I lean towards a thermostat problem. I am not an appliance repairman, but I did spend the night in a Holiday Inn Express once, and I used have an uncle that was the preferred appliance repairman in our town, his dad and my grandfather was also. I learned a bit from them.
If you search online there are places that have rudimentary diagnosis procedures and sell parts.
One such place is
www.repairclinic.com You will need your model number.
If you have a local appliance repair shop, they may be able to assist you. Unfortunately, most of those shops have gone by the wayside because of disposable appliances.
Good luck
Someone remind me to tell about how when I first met my wife her Maytag gas dryer wasn't heating...and I volunteered to fix it after I covered her house in lint...
Craig
99 I/S