There are various codes and standards on this issue. The one most widely quoted is NFPA 85C. It basically states that if the igniter (pilot) supplies less than 4% of the heater duty then is turned off after the lighting of the main burner.
There is basically two schools of thought on this. The first is that as long as there is a flame in the heater, then no large amounts of unburned gas can accumulate, so it is better to leave the pilots on.
The other is that unless you have a stable and self supporting flame then all gas going to the heater should be turned off.
I personally belong to the second school of thought for two reasons. First is by turning the pilots off, I can use the flame scanner to detect the main burner flame, and insure it is stable and self supporting.
Second is that it is possible for unburned gas to accumulate in a corner of the heater until it reaches an ignition source and ignites, which can cause damage to equipment, and people.
That same NFPA 85C states that if the pilots are to be left on they must supply at least 10% of the heater duty, and unles you bought the heater with Class 1 ignitors, then they most likely do not supply the required heat. The thinking here is that a large flame allows less unburned gas into the heater.
George Griggs
Sr Process Controls Engineer