From cold this morning, the boiler ran for a good half an hour, BUT with the thermostat on the very lowest setting. Once I turned the thermostat up (ever so slightly) the problem reoccured.

I tried it on MIN again, but as the boiler was already hot, it only ran for about two minutes, and then the burner and pilot went out.

RSD, November 2006

sounds like a thermostat problem, it is not shutting off at the right temperature so your overheat kicks in.
cant remember what boiler you said you had

BG MIKE, November 2006