check the pilot, look to see if the pilot is week. on most cases the unit needs a good cleaning. the pilot can become week because of debris in the orifice, when this happens it can allow the pilot to produce enough millivolts to keep pilot running but once the burner kicks on it pulls away from either the flame rod. or the thermocouple.
Most cases you can take a bottle of canned air and blow the pilot out. worst case is you take the pilot apart and get to the orifice and broach it.
If that is not the problem next step is to check the pressure switch. if the pressure switch does not open then you have a possible vent issue or pressure switch issue.
my guess is that this is a b-vent system and not a direct vent. meaning the dust and wood clogged the pilot up. when was last time it had been cleaned?