Baby chickens seem to be the issue... They despawn if you're not nearby, and also the number seems to be limited to 5. I've gone through up to 9 stacks of eggs, and can't get more than 5 baby chickens. I've used both a dispenser, and manually throwing eggs.
Otherwise I've got my 5 egg laying chickens that haven't disappeared at all on me.
All this means, that I can't harvest more than 5 chickens at a time, and have to hang out at the chicken farm to do so. If it was just despawning, then at least I could sit around and wait for 20 some chickens to mature at a time. So now I'm just basically building a ridiculous supply of eggs.