My hetaheat electronic 10/16 pilot light problems?

By boiler turns on fine (on timer) but after about 1-2 hours it switches itself off. When trying to ignite again, you can hear the fan going but the pilot light doesn't come on. It just clicks away without anything happening. I've had British Gas out a few times, they get it started and then it happens again in a few days. Can anyone tell me what is wrong with it and what parts I would need for it as I understand the parts are limited in range? Also, they have told me not (finally after 4 call-outs) that the 'board' needs replacing. Do you know what they mean by this?? Please help, I have a 1yr old and we are freezing. Much appreciated!!