Yes, bromeliads will only flower once and then begin to die. It could take quite a long time to die though. I have had some that took well over 6 mo. The pups are what you want to see, since those will grow to "adult-size" and flower. I have seen pups form months before flowering, during flowering, and months after flowering. That's why you should leave that post-flowering plant alone so that it has time to form a pup(s). When the leaves begin to brown, typically from the bottom leaves up, you can remove them just for esthetic purposes.
