Why does my furnace stop unless we remove and replace the inspection panel?
Sounds like the high limit might be tripping.  There are many causes for this, though faulty limit switch and/or dirty filters are the most common.

removing the access panel likely opens the door switch, so the unit is reset when the panel is put back in place.

Check for dirty filters, blocked/obstructed/closed return air vents, blocked/obstructed/closed registers. If you have the tools and knowledge to do so, inspect the high limit switch.