APOLLO BOILER KEEPS CUTTING OUT?

The flame on my Apollo gas boiler (about 20 yrs old) keeps cutting out after a short period of operation when the boiler stat is switched to 'high'. The pilot can be relit and is stable (I have replaced the thermocouple) and hot water or radiators will get warm on the 'low' setting and the boiler will continue to run. But when the boiler setting is then changed to 'high' (necessary for winter operation) the flame will fairly soon cut out and has to be relit. I have heard this may be due to a faulty 'limit stat'. Is this likely to be the cause, or something else? If so, where is it on the boiler, can it easily be replaced by a DIYer and where can a new one be obtained?