If they do run out of possibilities, ask them if the vent damper can be locked open. This can often be done through the manual set up control on the vent damper. Make sure they check the internal electrical connections for looseness on the switches that confirm that the damper is open. Damper lockout problems can also be mechanical from faulty vent motors, linkages or from the damper scraping against against the vent before it fully opens.
If your boiler then runs trouble free with the vent damper locked open over the next few days you'll know that the boiler lock outs are related to that part of your system.