Q. Centaurea - mine has bloomed well but is now flopping over. I see there is new growth, complete with buds, coming up in the middle.
There are many cultivars of Centaurea including annual, perennial and shrub forms. Judging by the conditions you mention, your plant is not an annual. The older growth can be prunned out when the plant is dormant. Yours is in active growth and should be prunned lightly if at all. Take out a few of the leggy, floppy branches and cut back more aggressively in winter.