GE links have a firmware problem which causes what you are seeing. It’s well-known, you will find much discussion in the forums and in fact on pretty much every other home automation forum. It’s the reason that the GE links are not on the official “works with smartthings” compatibility list. People used to buy the GE links anyway because they were much cheaper than other smart bulbs, but now that the hue whites are down to $15 at Best Buy, most people have moved away from the GE’s. If they are new bulbs and you can still return them, I would do so.
Meanwhile, the good news is that you generally don’t have to go through the whole remove and re-add process that you’ve been trying. You may be able to get them to figure out on their own that the network is still there with a few simpler steps. See the following FAQ. It won’t solve the problem, but it may give you an easier solution when it does happen.