It seems that if you are using DHCP for your server/DNS host assigned by the router, all of this breaks. I didn't remember you stating that your server/DNS host needs to have a static IP address assigned so that there is no lease to run out and that this must be done in your router.
Of course your DNS server needs to be on a static IP, or at least have a DHCP reservation. You also need to tell your DHCP server to actually give your new DNS server to your clients.