Thing is here – if your problem was a faulty thermocouple (and retired plumber should know better!) you would not be able to light the pilot light and keep it going once it had gone out. The thermocouple is a sensor device that when heated generates a very small electrical current which is sufficient to hold open a magnetic valve that allows gas to flow to the pilot light burner. When and if the pilot goes out for any reason the sensor cools down and as a result does not generate any electric current and as a consequence it shuts off the gas flow to the pilot burner.
From the description you have given I believe your problem lies not with the thermocouple lead itself but with the pilot burner which sounds like it is partially blocked up and not burning large enuff to heat the sensor probe of the thermocouple lead end.
If however, you check the pilot burner and it is burning with a clean blue kinda flame and is steadily playing on the themocouple lead head firstly check that the thermocouple nut end is firmly screwed into the gas valve – do not overtighten!!
It is possible but the problem although very rare may be caused by a faulty overheat device fitted into the internal workings of the gas valve itself – if this was to fail it would allow the main burner to heat up initially and reach temperature then click out the overhead device and shut down the gas supply to the pilot, which in turn would turn everything off, although the valve poisition would still remain in the “on” position.
Hope this helps you to understand the problem and I would suggest you get the services of a suitably qualified gasfitter to attend to your water heater – remember gas can kill!!!
Selgas Services Ltd
Craftsman Gasfitters, Plumbers, Electrical Service Technicians