LoL I Have the same problem , My furnace will only stay working if the filters are removed. We have replaced the thermocouple, gas valve and flu cap on an intertherm heatrite mgh-065-abwn-06. We have looked at the acoil and it looked clean on both sides on the top. There is a fresh air intake up next to the flu that we can feel some cool air, so I figure that's not plugged.

If I light the pilot with the filters installed I can get the furnace to start and heat for about three to five minutes before the flame shuts of and the pilot is out the blower will run for another minute or so then that's it have to light the pilot again.
Any help to solve my problem would be great ,I really don't want to run without filters thanks

After a night of running without filters the pilot did go out again...