My bachelor buttons have a couple with stems looking... alright, but the leaves have wilted and twisted. I have always wondered, If I chop the plant at the soil level, will the roots keep working and build up a new stem? Or is that the death of the plant due to nothing catchign the sun?
After reading your question, I decided to do a little searching online. Although I haven't read anything yet about the condition you say your plants are in (could be a whole different problem...insects or disease?), but I found several sites that say if you cut off Bachelor Buttons "right to the ground" after blooming, it encourages them to rebloom. With a healthy plant it apparently is good for it, but again, I can't say if yours are healthy.
If you can take a picture of one of them and post it in the "Garden Pests and Diseases" forum, there might be someone who could give you more info.