The oil burner can trip the reset button if the filter in the line from the oil tank is clogged, or if the tank is empty. If the reset button is pushed and the furnace comes back on, then the button resets again, the oil tank and lines need checked.
Just like diesel fuel for a vehicle, heating oil does have impurities. These sink to the bottom of the tank, creating a thicker sludge. If a heating oil tank runs low, the chances of that sludge getting into the fuel supply line are greater. The filter in the line gets clogged, the oil flow stops and the burner doesn't get enough fuel to keep running. The reset button trips because it senses the reduced amount of fuel.
Another scenario is if the oil tank is left to run dry. Not only is that sludge an issue, the burner is totally deprived of fuel. In both situations, the sludge tends to plug the oil nozzle. The nozzle turns the oil into a fine spray so it burns easier.
Unless a customer is familiar with oil burning furnaces, both scenarios require a service call. The oil lines need cleaned out, the filters need changed and the nozzle needs cleaned or replaced. Continually pushing the reset button doesn't solve the problem. It may make things worse by flooding the burning chamber with too much oil or fumes and causing an explosion.