The first thing I would suggest is to avoid British Gas - stories on here strongly suggest that they are money sharks and use all sorts of wicked techniques to scare customers into spending money - you would do well to ditch them. When they behave ethically - and I'm sure they do from time to time - they're very expensive.
Your boiler is being "told" to fire up because the Pilot Flame is burning - for some reason the main Gas valve is closing prematurely. It is quite possible that the control electronics (pcb) is closing the gas valve because it "thinks" the pilot flame has gone out - if this is the case then the fault may be a defective pcb (about £120) - a partially blocked pilot flame injector (about £40) or a poor connection between the pilot flame sensor and the circuit board.
My guess - and it is only a guess because I'm an unqualified and inexperienced muppet - is that the control board has a heat-related fault - all is well when the pcb is cold - the boiler fires up as it's supposed to - the pcb gradually warms up and the fault (whatever it may be) closes the main gas valve.
If it were my boiler I would inspect the pcb for badly soldered joints or replace it. You may wish to call in an independent gas safe engineer.
Here's a link to a guy repairing his own pcb for a few pounds.
http://kaijaks.co.uk/blog/nick/2008/02/10/dodgy-old-boiler
Take my answer here with a pinch of salt - I stress that I'm inexperienced and unqualified to provide any accurate or worthwhile help - just a retired computer engineer.
Good luck
Peccavi
March 2010
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