While this is true for the Kensai's signature weapon, it is not true for an Ancestoral Relic.
Nothing in the text of either Ancestoral Relic or Annointed Knight indicates that the effects only work for the character himself or while the character is alive.
In fact, the Annointed Knight Ancestoral Relic abilities are listed as permanent and the Ancestoral Relic feat states that the weapon gains those abilities, not that the weapon in the hands of the owner gains those abilities.
As for why this happens, a Kensai gives up XP to enhance his weapon. Although this is upwards of about 3/4ths of a level at high level, he will typically gain some of this XP back when he is a level lower than some of his fellow PCs and hence, gains more XP for the same encounter. And, a Kensai should have more magic items than others in his group since he does not pay gold or wealth for his magic weapon.
An owner of an Ancestoral Relic gives up a boatload of gold/wealth in order to enhance his weapon. It is twice as much gold as someone with the Craft Arms and Armor feat and it is limited to one specific weapon, but zero XP. All in all, this is a pricey feat, so the item should be permanent.