Bromeliads grow a rosette, mature, flower, and the rosette dies. Some make offsets before dying. This species usually makes one offset just as it is dying. Don't give up; continue keeping it evenly moist.
__________________ May the bridges I've burned light my way.
It's not dying, it's just done blooming. When the flower bract dries up it can be removed. In the mean time it will probably start to grow a new pup from the base of the plant. Just continue to care for it as you were.