Fuel oil burner running intermittently
Is this in a boiler (steam or hot water heat)? Are you getting any heat in the house?

Assuming yes and yes, this can be normal operation. In a boiler, the burner heats water to a set temperature (e.g. 160F). When that temperature is reached, the burner shuts off. To actually deliver heat into your home, there is usually a circulator pump. This takes the hot water in the boiler and moves it through your radiators, which release some of the heat from the water into your home and send cooler water back to the boiler.

If your heating system can't keep up with demand, it can be because the boiler can't make enough heat, or because the radiation can't distribute it quickly enough. It sounds like your limiting factor is the radiation, which is not unusual. So even though your heat is constantly on, it is being distributed as quickly as your system can currently manage, and that is slower than the burner can produce heat. So the burner gets to take breaks.

A few options to address this:


Confirm that all radiators are hot; if some aren't, they may have their valves closed or be air-locked and need to be bled. Steam radiators may have defective air vents.
Increase your boiler's water temperature (probably not higher than 180F, though the design max temperature depends on your particular system and may be higher or lower than that)
Check that your circulator pump is working properly. Some have multiple speed settings, so you can try increasing that to increase water flow through your radiators.
Add radiators.