The gemara says that when you cover it with ashes and the flares up again, it is sufficient. The gemara rejects the notion that when it flares up it is הדרא למילתא קמייתא as if it were never covered, but it isn't clear whether it has full status of being covered. Tosafos d.h. Shema Minah, has two approaches. The first is that קטמה והובערה has the full status of קטומה and one is allowed to place even something that has started cooking and hasn't yet reached מאכל בן דרוסאי. However, the second approach of Tosafos compares the language of קטמה והובערה to the language of the gemara earlier קטמה ונתלבתה, and explains that קטמה ונתלבתה means that it regains some strength but the original covering of the coals with ash is still recognizable and therefore is considered fully covered to permit shehiya and chazara. But the language of קטמה והובערה implies that it flares up fully as if it were never covered and therefore only permits the leaving of a food that is fully cooked but is נצטמק ויפה לו. It will not permit the leaving of food that has not been fully cooked acc. to Rabbonon, or food which hasn't yet reached מאכל בן דרוסאי acc. to Chananya.
The Magen Avrohom assumes that even if it flares up back to the way it was, we can consider it like ketuma completely, and permit shehiya and chazara as we would if it were ketuma. R. Akiva Eiger disagrees and requires us to be concerned for the second approach of Tosafos and it would only allow the shehiya of a food that is fully cooked, even if it is נצטמק ויפה לו, which without גרופה וקטומה, the Rabbonon who disagree with Chananya would normally not allow.
The rationale for the second approach of Tosafos seems to be that the concept of נצטמק ויפה לו or נצטמק ורע לו is really subjective. As we see at the very end of the gemara, if one needs the food to retain its shape and quantity for guests, it is considered for him to be נצטמק ורע לו, even though for others it would be נצטמק ויפה לו. Therefore, by going through the motions of covering it with ashes, one shows that he considers the additional cooking to be נצטמק ורע לו, even though it is objectively נצטמק ויפה לו. That is why even when it flares up, it is still permitted to leave the food there, because he has already shown that he considers it נצטמק ורע לו by placing the ashes. The fact that it flares up doesn't undo what he has shown. But, food which has not been fully cooked is very objective, therefore, if the היכר is not longer there because it has already flared up, one can not leave food that hasn't been fully cooked since we are afraid he will stir the coals to raise the temperature and make it fully cooked.
This raises and interesting conceptual point. Is the purpose of גרופה וקטומה to have a היכר that is recognizable and will remind someone not to stir, or is it merely to do an action that reveals that this person doesn't care about extra heat and therefore won't come to stir the coals? It could be dependent on the two approaches of Tosafos. The first holds that if the action is done, that is sufficient even if it is no longer recognizable, whereas the second approach holds that if it isn't recognizable it isn't considered קטומה (just that we permit נצטמק ויפה לו since we consider him to have revealed to us that for him it is נצטמק ורע לו).