What i say may not be the issue, but on top of the cylinder there should be a draft diverter, that needs to remain clear at all times, so many people put their clothes around it to dry them off, the effect of that is the products of combustion dont leave the flue to atmosphere and in some cases where downdraft occurs can snuff out the pilot due to lack of air for combustion;
The thermocouple is the usual fault and they are cheap as chips to buy and simple to fit, but in doing so one might aswell as part of a routine clean/check the pilot injector, after assembling and checking for leaks on any pipes undone,ie. the burner and the pilot tubes light it up and adjust the pilot length if it is bigger than a bic lighter flame its more than likely impinging itself on the thermocouple, again upsetting things, all very simple stuff, your main burner should come on and stay on till the water reaches temperature then the burner turns off leaving only the pilot going, just to clarify the burner doesnt go all day its whats refered to as snap-acting not modulating like more complex appliances.