It could just need routine service. If mine goes out twice it means that a service is required, then It works fine.
You are probably suffering from the change in standards of heating oil that occurred towards the end of 2008 when we changed from the old British Standard for kerosene to the new EU standard which drastically reduced the amount of sulphur in fuel. This has the effect of causing increased sooting and carbon build up around the fuel line and wick of an Aga or Rayburn. Over time this carbon build up restricts the flow of oil from the fuel line and eventually the oven becomes starved of oxygen. As a possible solution, I recommend the use of a fuel additive which can counteract the effects of low sulphur content and clean your carbonised Aga have a look at http://www.ecofuelplus.co.uk/#/aga-rayburn/4539905465
or Aderco 5000.
Spillage
There could be a draft causing the pilot light to go out.
Check your instructions, Usually you have to keep it on pilot mode for 30 seconds then you should be able to turn it to on without the pilot flame going out.
A small amount to keep the pilot light going.
Spillage excessive condensate bad thermocouple draft
My direct vent furnace pilot light issue was the glass viewing port was missingallowing room air to blow out the pilot light. Replacing the missing glass which stopped the draft, fixed the problem.
There are a couple common reasons for a pilot light going out. 1. The thermocouple is weak. This is the gold rod that must see the flame in order to keep the gas valve open. it is a safety device that will not let the gas vavle open if there is no pilot. 2. The pilot is dirty and has a yellow flame. If this is the case, it will have to be cleaned. There are books on he market such as forced hot air furnace - troubleshooting and repair that show you how to repair your furnace. You can buy this at amazon.com
No, that is part of the function of the pilot light. To light the burner and to keep the gas valve open. The thermocouple sits in the flame of the pilot and produces a small electrical current that keep the gas valve open. When the tank cools down, the thermostat opens the valve to the burner so that it can light. When the pilot goes out, it is usually the thermocouple that is bad.
If holding the controls in the LIGHT position for about 15-30 seconds does not keep your pilot lit, there is probably a problem with the thermocouple. That is the small tube that the pilot flame touches. Be sure it is not bent, and being missed by the pilot flame. They do go bad, and require replacement.
The thermocouple is going bad. The thermocouple is the small tube that sits in the flame from the pilot light and goes back to the gas valve. They are easy to replace and cost $6 to $8. For health and safety the failing part should be replaced without delay by a competent gas engineer.
It is supposed to quit burning.
If this is happening you need to get your furnace serviced by a qualified engineer.