Once we light the burner and it heats the water and the burner goes off so does the pilot light. We just bought the house and have only been here 2 weeks

How are you going about " we light the burner "

Hi Cawebb

How old is the water heater? If you don't know, post the first 5 letters/numbers of the water heater serial number (no more than that though so no one can claim your warranty, if available) and the name brand and we'll see if we can find out. The serial number should be on a tag on the heater at about waist height... ;)

Once we know the age of the heater we can tell you if this is a combustion/air make-up issue or something else, OK?

Mark