It is a common misunderstanding that bananas die after fruiting, they do not. The shoot that was fruiting will die back, but the plant as a whole will continue to grow and fruit indefinitely by the production of suckers. If you are saying that your fruiting shoot does not die back after fruiting, that would be perhaps because you are not waiting long enough to observe the process. After harvesting a bunch, the shoot that had the bunch can remain alive for awhile longer but will not grow any more leaves, and will eventually die back. There is no type of banana in which the shoot continues to grow and produce more leaves after fruiting.
In some extremely rare cases you can have multiple shoots forming one pseudostem ("trunk"), and it can appear as though the single shoot is continuing to grow after fruiting, but in reality they are different shoots, however I highly doubt you are observing this type of situation.
There is no way to ID your plants without photos, so please post them for an ID attempt.
Growing bananas in Colorado, Washington, Hawaii since 2004. Commercial banana farmer, 200+ varieties.