The general advise is when you're dividing rhizomatous irises (sibirica, ensata, but especially germanica/bearded types) to throw away the old rhizome because it wouldn't bloom anymore.
Has anyone actually ever tested this?
I can understand that new sections have a supressive action on the old rhizome (comparable to apical dominance along a stem, but this is just a guess...) so that would explain why the old rhizome won't produce leaves and blooms. But once they're separated, what holds the old part from growing and blooming again like before?