Again & Again is a funny bird. It likes to get moved after Spring time and this will prompt it to bloom again that year. You need to either speed up the bloom process for the Fall (more fert and water) or try and go the other way and put it into a drought situation. I have had little luck in controlling it (though this year I will not get any Fall/Summer re-bloom from "Again & Again").
The fact that I get "re-bloom" throughout the Summer on "Again & Again" indicates that the increses on the Fall bloomers are not mature enough to bloom in the Spring.
You can not "save" the mother rhizome. A expert (botany) would need to tell you if cutting the stalk would push the plant to put it's energy into the increases. My guess is that it would have a minimal effect; but that is just a guess.
The best way to "re-start" a re-bloomer is to dig it up in July and do not put it back in the ground until September. No pot, just sitting in the garage loose.
Remember; most of my experience is with re-bloom happening without the extra help I should be giving.