IPOfficeNewUser,
DHCP Clients (the IPO) are suppose to go back to their DHCP server (Cable Modem) and ask to renew their lease half way through the lease duration. So if your cable modem issues a DHCP lease with an expiration of 24 hours, then at 12 hours the DHCP client should ask to renew.
I presume you have the WAN/LAN2 port of the IPO on the Cable Modem and set as DHCP Client, and the LAN1 port of the IPO going to your LAN Switch?
Where are you located? In my area cable modems use DHCP, but the IP address never changes unless the device plugged in to the modem changes (thereby the modem seeing a new MAC address).
If it becomes a big problem, stick a NAT Firewall/Router in between the IPO and the Cable Modem and let the Firewall/Router deal with the DHCP on the Cable Modem... our get a Static IP if available.