Is this an older printer or a fairly new one that has Wifi capability ? Because you lose the internet for whatever reason you shoulkd not lose the printer off the network.
he printer I have has an install cd that has an option to connect wirelessly and I have it connected to the network by wireless and that means that it's connected to the router and not a specific device like a laptop or desktop. Once the drivers are loaded then it should stay loaded and not have to keep loading the drivers.
If your internet drops because of your router then maybe it's time for a new router because you shouldn't have to keep loading the printer.