Note: I will be revealing locations here so if you want to find the note on your own, there be spoilers ahead!
Last night, I was running with a friend, I was host. We walked past Kairness and I asked if he wanted to pick up the Nimrod quest, and ducked into the house to grab the note. I'd done it once before at this point, over 24 hours prior. The note was not there. We both checked in soul mode, shrugged, and went on.
Tonight, he messages me that the note showed up for him. I run to Kairness in my own instance (solo) and the note is not there. I relog for good measure and check again. Still no note. I join his instance, the note is there. I drop party and respawn in my own instance, and the note IS there. I decide to relog and see if the note stays. I return to Kairness after relogging and the note is gone again.
I don't know if this has any relevance to the issue at hand, but apparently when I dropped party, a copy of my Birb stayed in his instance with him.