Considering how bad at English are the people that work at Oasis that they translate word for word rather than what makes sense, then the word "persists" can be interpreted in more ways than one, such as the effect of stacking up keeps going instead of freezes and leaves the buff at the % before Kushina died. In such sense the "persist" makes sense as well, because the buff of consuming each time 10 chakra "persists". So it's up to the testing whether it works or not after Kushina is dead, but it has to be tested on ninjas who do not passively or actively buff themselves, so that results are cleaner.

I have the Christmas Kushina, got it today, but I might try to test her later in the evening with someone, so that I can tell if ninjas keep buffing up after her death, or the buff gets frozen at the last % that got buffed.

I tested yesterday with a group member, I used regular Naruto for testing, he was skillbooked, but he has no scaling skills, and I used Kushina of course. After Kushina died, Naruto was dealing ~830 damage with his standard, after the next mystery launched or two, his standard was dealing ~870 damage, and it was long after Kushina was already dead. So I think the scaling of the Kushina Christmas passive, when ninja consumes chakra, stays in effect after her death.

The effect does not freeze when she is dead, meaning that the % buff you gained before she died, is not staying at that %, but instead keeps increasing after her death every time your specific ninja consumes chakra.