Is it necessary to repeat a prayer after performing it unintentionally without ablution?

Yes, whoever prays forgetfully without ablution must repeat the prayer, because the Prophet, peace and blessings be upon him, said: "Allah does not accept the prayer of anyone of you if he passes wind until he performs ablution." As for whoever prays in a ritually impure garment forgetfully, he does not have to repeat the prayer, because the Prophet, peace and blessings be upon him, took off his sandals during prayer when Gabriel informed him of impurity on them, and he continued his prayer, which indicates that one who is ignorant of or forgetful about ritual impurity is not commanded to repeat the prayer.