If an IP phone could not renew its lease at half lease time, it would keep on trying periodically until the lease's end. At that point, it surrenders its IP address, and is not usable as a phone until the DCHP server comes back.
But, while the lease has not yet expired, if the phone is powered off and on again, it will boot up without being able to get a DHCP server's acknowledgment to the phone's DHCP request. The phone would then assume the last known good DHCP scope, and not start the lease timer until a DHCP server was heard from. In other words, it would come back up and stay up forever if no DHCP server were to appear.