I'd be inclined not to divide it, at least not now. What may have happened is that the main core of the plant has had some sort of set-back, and the healthy leaves you are seeing now are from the outer growth points. If it has had a set-back that has stopped it flowering, the main plant needs the energy it's now getting from these, to recover; if by dividing it now you remove some of those vigorous bits, you risk starving it of that restorative energy.
If all seems well, and if you really want to divide it, the best time would be at the start of next autumn's new growing season, when its new roots will be at their most vigorous.