I believe this has something to do with MAC address of the router, as the modem stores such information and makes a lease query based off that address (the modem itself most likely doesn't receive own external IP, yet in most cases accessible via web-interface - i.e. http://192.168.100.1 for Motorola models, google for your make. For this, I presume, you must be directly connected to the modem with one of your systems). One of the ways to resolve it would be spoofing router's MAC (if possible at all), another - reseting the cable modem to the factory default to clear MACs stored in modem's memory, which is easier to do via web-interface, but I wouldn't recommend it without notifying and hence receiving a blessing from your ISP first, as I'm not a professional and have only a vague understanding of the consequences, moreover never tried it before myself. As for what can you do to make the IP release/renewal easier next time - as far as I understand there is nothing to be done on the user side except what was already mentioned: reseting to factory defaults or spoofing router's MAC, which is probably not that easy to do, if that option is not openly available on your model.
install the ddwrt firmware on your router iw will solve your problems .http://www.dd-wrt.com/dd-wrtv3/