Well, every direct vassal gets a vote on who is the next clan leader, yes? In my last game I had given out no dayimo titles, except to my own sons. I had some others, from conquest, but big majority of my direct vassals were kokujins. Now for some reason, suddenly almost all of the kokujins decided to vote for another guy as clan heir, a kid at that. Luckily this was at the very end of the game, so I managed to win before it became a problem.
Also weird in that, was that that particular guy kept taking new provinces.. and keeping them. He had 20, personally, at the end there. Thinking back, I'm not sure if he was a dayimo or not, which I suppose would explain it. He could have a very large retuine, so when I fought wars (and I preferred to rely on retuines), he took a lot of new provinces. If he wasn't dayimo, he couldn't hand them out.