There are several occasions where the fire burns low or burns out in Lord of the Flies. The first fire the boys make in chapter 2 is a huge bonfire that reaches twenty feet high, but it "diminished quickly; then the pile fell inwards with a soft, cindery sound." This is on page 46 in my copy, but if you have a different version, it's just over halfway through chapter 2. Unfortunately, the fact that this fire has burned low is deceptive; it soon catches again when it spreads to the "great patch where they had found dead wood" and engulfs a huge section of the island, killing one of the little boys.
In chapter 4 Jack takes Samneric away from tending the signal fire, and Ralph finds that it has died just as a ship passes the island. In my version, on page 77, it says, "The fire was dead." This is just over halfway through chapter 4.
At the beginning of chapter 6, Samneric have been on night duty tending the fire, and it almost goes out while they sleep. One of them says, "I believe it's out." However, the twins work together and get it going again.
On page 194 (my version), about halfway into chapter 10, the remnant of Ralph's tribe tries to keep the fire going, but it's too much for them. Although three boys have just loaded the fire with rotten wood, producing smoke, by the time they get back from gathering fruit, "only embers glowed in the fire, and there was no smoke."
Keeping the fire going is a difficult job, and there are several times during the book when the fire burns low.