I feel I need to chime in and explain how DHCP works since it's my background.
When you're leased an IP by DHCP, unless a specific rule is set to not lease the same IP, the DHCP server will always give the same IP out again. It'll also actually start the renew process halfway through your lease time. Example, if you have a 4 day lease, it'll actually renew it in 2 days (or attempt to anyway).
That said... it's actually in RCN's best interest not to mess around with settings and make changes to the IP address. There's no reason too and if they added special rules it just makes for something else to go wrong.