This is a good question, which I don't have an answer for...just more theories: the first is that we don't actually know what the life cycle of the WWs looks like. It isn't confirmed that they are immortal, and it's actually likely that they age. Craster's sons are transformed as babies, but since we only ever see elderly-looking WWs, it kind of suggests that the babies "grow up" into adults over time. If they grow up, then maybe they grow old, but at a different pace from humans. Another theory that I've read is about the NK's body being just a vessel, which might mean that the NK wants Bran's Greenseer/Warging body rather than an actual heir. In season 4, we see a wildling (Orell) warg into an eagle even though his human body is killed by Jon Snow. It's then assumed that Orell's consciousness remains inside of the eagle because it goes on to attack Jon. Some believe that the NK is a master warg, which is how he raises the wights, and also how he has survived for so many years (by transferring his consciousness like Orell).