Alternately, you can go into the Advance setup of the modem's HTML pages to renew the IP address. If you are running "RFC 1483 Bridged/Routed" encapsulation, you can go into the Wan status of the Advance Setup and click "Release/Renew" to refresh the IP address. If running a PPPoE/PPPoA encapsulation you would need to go into the PPP status page of the Advance Setup and click "Connect/Reconnect" to refresh the IP address. You should also verify that "Automatic Reconnect" is checked as well.
The modem will not automatically put in a request for a new IP when the physical connection is re-established. This is because the modem has retained the previous IP address in memory and will wait for the remaining lease time to be over before putting in a request for a new IP address. The average lease time set by most servers is usually 3 days, so whatever time is remaining from the original request of the 3 day lease is the time the modem will wait before asking for a new IP address. Many times this will not be necessary as the ISP usually reassigns you the same IP address if still available and you will be able to reestablish the connection with no further ado. But sometimes, when it does not, you will have to manually put in a request to renew to get a new IP or power recycle the modem in order to be able to fully re-establish the connection.