Wallygater; a bit more detail of what is happening might help to understand your problem.
When the burner shuts off is the thermostat still calling for heat?
Or are you saying the burner will not start at all even when the thermostat stat is actually calling for heat?
How does the burner operate in the DAY time?. Do you have a "set back" thermostat stat that lowers the temperature during the NIGHT hours?