Hydroponics plants will grow through their natural cycles. Annual plants will grow until they've matured and will die at the end of their growth cycle. Other plants will continue to grow as long as their needs (water, nutrients, sunlight, temperature) are met. Since hydroponic plants aren't subject to the same stresses as field-grown crops, they can often be started early and then continue producing for an extended season.
Even long-lived plants, like perennials and even trees can be grown hydroponically, so there is no artificial limit on the lifespan of a hydroponically grown plant.
