The question is often asked: How could God harden Pharaoh's heart, denying Pharaoh the right to repent and thereby avoid punishment? It is usually explained that in the first five plagues Pharaoh hardens his own heart, and only from the sixth plague onwards is his heart hardened by God. So in fact he had many chances to repent, but eventually the sin became so ingrained in him that it was not realistic to talk of his repentance.
While not incorrect, I find this to be a weak formulation of the real answer. For it was not only during the plagues that Pharaoh had things to repent for, and chances to repent. Were the plagues a punishment for not letting them go worship God in the desert right now, as Moshe requested? Is that the only thing Pharaoh did wrong? What about the slavery, the killing of babies, and so on?
It may be that the content of the plagues hints that they were punishments for these earlier and greater sins. One wonders if the Egyptians, confronted with a bloody Nile, remembered the babies they had thrown in it. Or when their food supply was destroyed by locusts and hail and they probably had to buy food from neighboring countries, if they thought of their ingratitude towards Yosef's descendants. These plagues seem like "measure for measure" punishment for injustices that reach back centuries.
After the plagues, letting the Jews go celebrate a holiday would not have been repentance, but rather self-preservation. God hardened Pharaoh's heart to prevent such an escape from punishment. But there was no need to harden his heart to prevent repentance for the earlier deeds, because Pharaoh never considered real repentance for them. Even before his heart was repeatedly hardened, he never offered to end the slavery, only to let the people leave for a few days and then return.