Water Heater pilot light blows out after burner ignites!
Check the flue area from above the flame to the flue pipe, the flue pipe, and the chimney for any type of blockage or flow restriction such as a build up of dirt, rust, soot, or even a bird that may have gotten into the flue pipe or chimney.If you do not get rid of the burned gases the flame will go out slowly as the available oxygen is depleted. It is also possible to have a bad heater control, but I would check the flue first. The problem is probably not the thermocouple since a thermocouple will still produce voltage for some time after it's flame goes away.