If this model has low oxygen
shut off it probably depends on pilot flame burning high enough to maintain the thermocouple temperature. Safety feature as low oxygen
would cause less height in pilot flame, so furnace
would shut down.
Question: Does the pilot stay lit if the furnace
does not cycle? If you light
the pilot with the thermostat turned down too low for furnace
to come on does the pilot still go out shortly after?
If so one can eliminate anything to do with thermostat cycling the furnace.
Might look at venting if the furnace lacks sufficient venting and is using up the oxegen when it runs it could (and should) cause the pilot to have a smaller flame so it can't heat the thermocouple.
Might try cleaning the thermocouple end where pilot heat is applied and maybe the pilot burner itself as low cost general maintenance.