The lifespan of your slackline will often depend on the amount of use it gets, the weight and physical condition of the person using primarily (a slackline used by an adult will wear faster than one used by a child), and the amount of tension that it is usually kept under. It’s best to inspect the slackline regularly for signs of wear, the thinness of the material, discoloration, or fraying, and if you see any of these, be on the safe side and consider a replacement.
That being said, depending on the material of construction, your slackline, even without signs of wear and tear should last somewhere between five and ten years, so if it’s getting to be about that age, consider replacing it.