why won't my pilot light stay lit?

I have a Baxi Central heating system, there is no model number. The pilot light under the fire won't stay lit for more than a few minutes. I light it using the grey push button then reapetedly pushing the ignitor button until it goes on. the pilot light goes off again almost immediately unless the heating is on, and even then, it only stays on for a few minutes.I live on the top floor flat.