Why is the pilot on my GE water heater turning off when the burner turns off?
'Gusting" of the combustion air can be caused if the shrouding around the base of heater is loose or missing.  Such gusting can knock out the pilot.
Another cause of pilot extinguishing is a too rapid start up of the main burner.  Usually there is a small baffle around the pilot, protecting it.  
Too high a pressure of the gas would also cause a too large main flame.  This would have to be checked at the meter by a qualified technician.  This, obviously, is a dangerous condition.  Other gas appliances (gas stove) might reveal this condition.
Conversely, too low a pressure (and therefore, low gas flow) might make the pilot more sensitive.


Once the pilot is knocked out, cooling of the gas valve thermocouple will prevent restarts.