Pilot going out

I can light the pilot, set the dial for the level I want and the burner will light OK.
After the heater gets up to the temp it's set to and goes out the pilot will fade out and extinguish. I can re-light the pilot again, holding it down until the sensor heats up, but when I set the dial the flame shrinks and goes out again. Once the heater has cooled down I can light the pilot and it will stay lit and cycle the burner again, but will shrink and go out once again after the heating cycle shuts down. I have taken the lines apart and blew them out, along with the pilot tube, to make sure they're not blocked with dust.No change, still does the same thing.

Any idea why?

Thanks,

Dan