Liatris, (mine at least), doesn't usually branch. It grows from a fountain of leaves on solitary, leaf-less flower-stalks. You may have purple loosestrife, which looks similar, but can branch and has leaves that often form at the bottom and continue in whorls all the way up the flowers stems. Check out some pictures of purple loosestrife to see if this is what you have, here is, I believe its scientific name: Lythrum salicaria .

Since having posted my query, I've talked to a horticultrist who told me that it is an anomaly that she's seen a couple of times. It's definitely liatris. The bottle brush appearance gives it away. I can see the brushy leaves starting to turn brown and drop off. I just wondered if that was part of the blooming process - loose the leaves as it starts to put on buds. I just wasn't sure if it was dying or not. Guess I'll learn this all on my own.