There were two different types of anointment: one for Aharon and his sons which inducted them into the kehunah, priesthood, and one which was only for Aharon, which elevated him to the Kehunah Gedolah. The first anointing, which included Aharon and his sons, was eternal insofar as it was performed once and was sufficient to consecrate the status of kehunah for posterity. The second anointing, however, served to sanctify only Aharon for the Kehunah Gedolah. His sons, however, and all future Kohanim Gedolim were required to undergo another anointing.
Horav Mordechai Gimpel Yoffe, z.l., explains the reason for the distinction between the two anointments. Anointing Aharon and his sons for the kehunah was the method by which the kehunah was consecrated for posterity. Hence, any male born into this family would automatically be considered a kohen. Regarding Kehunah Gedolah, however, only when the son was spiritually suitable to succeed his father might he ascend to the position of Kohen Gadol. Otherwise, they would nominate another kohen to assume the position. Hence, the appointment of Kohen Gadol was recreated each time and would subsequently mandate a new anointing. The Kohen Gadol’s position was one in which the individual had to be uhjtn kusd, “highest among his brethren,” a distinction which had to be earned, not inherited.