According to Megillas Sesarim, Achashverosh is concerned that annulling the decree would lead his people to say that not only is the king fickle, but he is also playing favorites. Historically, nepotism has been a legitimate cause for rebellion. Many wars have begun over the choosing of an undeserving successor.
R’ Avigdor Bonchek writes that Achashverosh is afraid to annul the decree because he is overcompensating for his own fickleness.
In accordance with the previously mentioned opinion of the Rema (see #458 above), there are things stamped with the seal of the King that cannot be changed. There are sins for which teshuva (“repentance”) can gain atonement, but will still not be taken back, like chillul H-Shem (“debasement of H-Shem’s Name”). The Rambam (Mishneh Torah, Hilchos Teshuva 1:4) writes that such a sin can only be overwritten by a diametrical act of Kiddush H-Shem (“sanctification of H-Shem’s Name”).