Any bulb that you plant will only live for a few years, but don't despair. Before it dies the original will have produced offsets which continue to grow and become the replacement bulb(s). As a gardener you will not notice this happening because you will (should) get a display of flowers year after year for many years to come.

As bulba says they technically do die out but the offshoots take over. if you grow asiatics in pots when you repot them put the offshoots into a 'nursery pot' then you can feed them regularly to build them up. if they are in the ground then let mother nature take its course.
I have mine in pots and this year I hade 15 offshoots and they are all in a 3 litre pot and will go outside infront of the garage to do there own thing. the biggest bulbs will go in the bedding 'display', in their pots which I bury into the ground. when they finish flowering I lift the pot and put in something else.

In fact, Asiatics have been known to become invasive, if they like where they are!