I used to grow bromieliads, so here's what I think is going on. The flower on the mother plant blooms for several months and it will die. The mother plant only flowers once. In the winter do not put any water in leaf cup but let it dry up, only you must be sure the plant is in a nice warm humid environment. Return to watering the cup at the beginning of the growing season. After the flowers death the mother plant will start producing little plants around its base. At this time you will start to see the mother plant start to slowly die and rot. Do not separate the baby plants from the mother as the are utilizing the mother plant for nutrients to sustain their growth. When the main plant is completely rotten then you can separate the offspring and plant each one separately. There are those who have been succsessful in getting the main plant to flower twice by placing the plant in a plastic bag with an apple for a few weeks- the ethylene gas produce by the apple inducing flowering. I tried it a few times and had no positive results. It is a marvelous low care houseplant isn't it.

Since I live in a warmer area, I grow mine in a woods. There is one that is in flower now, and it gets lots of rain water. Another one flowered in August, and has pups which appeared about a month after it finished flowering. I would have thought it would be better to keep watering it until the pups appear, and then take care of the little ones and ignore the parent plant until it dies; and to keep everything frost free. The important thing is to give the new ones time to grow to flowering size. A friend had bought one, and when nothing happened after a couple of years, he gave it to me. I divided it, but it takes a couple of years to get a flower. But like I said, my experience is growing them outdoors.