The issue is more a request to further balance the fire because it does break immersion some, rather than any sort of bug. Perhaps add another texture that shows the pit as gray and the heat waves replaced by wisps of smoke once the fire pit has gone beyond re-ignitable.
Also, allow the fire to be rekindled with smaller sticks, items of cloth, anything flammable combined with the blowing animation rather than having to create another pit on top of the old. I didn't even try that though. Can a fireplace be placed on top of a old one? If not, can an old fireplace be broken up and displaced in order to place another pit in its spot when space is limited?