I can give you a few suggestions, but if these aren't the culprits, you may want to check with a professional, as you would be talking about altering or replacing safety components. First, check the door to see if it has a switch, making sure that the door is closed for the unit to operate. Sometimes, if the door isn't fitting snugly, or if the switch is faulty, the heat of the fire can move the door, causing the switch to go off. As it cools down, it moves back and makes contact with the switch again. Push in on the door (be careful not to burn yourself), when the fire goes off, and see if it comes back on. There could be a loose wire, somewhere in your system. The last option I can readily think of, at this time, would be the thermodynamics of how these systems work. As the flue warms up, it tends to draw better. This can cause the flame to grow. As the flame lifts, the pilot flame also lifts, leading the thermopile (sensor) to not feel the heat and so shuts off the main burner. When the draw decreases, as the burner flames cease, the pilot heats up the thermopile again, and the flames return. You can either adjust the pilot or install a piece of metal above the pilot, to keep it from lifting. Hopefully, one of these solutions will solve your problem.