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If it's getting too much shade that could cause it to not bloom as well as to get floppy. If it's never bloomed it's unlikely it has anything to do with needing to be divided...sometime in years previous when it was smaller and didn't need to be divided yet it should have bloomed if the other conditions were right for it.
Might be a good idea to give it a haircut, that generally cures the floppies. I was told to do this to my Autumn Joy, and I did so with bated breath, I was sure I was killing it. But, it worked like a charm, got bushier at the base and could hold up the flower heads much better in fall. It used to get about two feet tall and flop over , now it gets to about 18", after I cut it back and it regrows, and fills out great.