system cuts out after 20 seconds?

i recently had a plumber out because we decided the diaphram wasnt the problem.he removed the pump which had some pieces of carbon in it and replaced it with a new one.he fired up the system but unly the nearest radiator got hot.he said you ma have to flush the system.so with a relative we emptied the system and ran water through the whole system twice draining out of the furthest radiator,we DIDNTuse any addatives, we then refilled the system .bled the radiators and fired it up,hooray all the radiators heated up.but when the system turned off at the night ,the next morning the same problem again,only this time not even the nearest rad got warm,the system fires up for about 20 seconds then cuts of.