I find this very interesting. What can make these incompatabilities happen, othere than chromosome count?
I don't know for sure, but I've always sort of assumed that it must have something to do with the relatively strong self-incompatibility of most beardeds. I haven't checked this but that's what I've been told anyweay. I don't know if it's the right system for bearded irises, but I've read that in some other plants, the pollen won't grow down the styles if it has an incompatibility gene that matches one of the incompatibility genes that the pod parent has. The plants own pollen would always have a match and so would always be not-compatible. Offspring would have at least half of their pollen matching (and so those pollen grains would be incompatible), sometimes all would be incompatible. This system helps ensure that outbreeding to unrelated irises will occur.
Another thing I've noticed is that I can cross certain species only in one direction. For example, I was able to cross Iris pallida 'Kupari' with Iris variegata only by using the pallida as the seed parent. Why it is this way, I don't have a clue but I know that it also happens in other plants. It's referred to as "unilateral compatibility" if you want to try to find out more.
So, I try to just remember these difficulties and plan my crosses accordingly. But as soon as you think you've got something figured out, be prepared for more surprises! ;0)