I have an older Armstrong forced air furnace. Pilot ignites the burners, blower motor runs then burners shut off. Control board is operating, thermostat is operating. There does not seem to be any condensing drain issues. Now what?

Im not completely familiar with this brand, but if it has a flame sensor, cleaning it will likely solve the problem. If your unit is new enough to have condensing drains, it most likely has a flame sensor.

Does the pilot stay on all the time or only when the thermostat is turned up to call for heat?