I thought, once we got the 3 Black Oaths, the reason was obvious enough why the 'hour of my death" clause is present:

1) I shall obey all commands given by those placed above me in service to the Great Lord; 2) I shall prepare for the day of the Great Lord’s return; and 3) I shall hold close the secrets of the Black Ajah, unto the hour of my death.

1 and 3 contradict each other, if, say, a Darkfriend placed about you orders you to reveal all the Black Ajah's secret. If they swore to never reveal those, period, the two Oaths would contradict, and the Black sister would fall dead.

The "hour of my death" clause gives you the out. Since failing to follow the orders of this person would kill you, the "hour of my death" clause allows Oath 3 to be subordinate to Oath 1. That's why that clause exists.