why is your router renewing IPs daily
This is quite common among many ISPs. These providers require a dynamic IP address be used. This is to prevent the customer trying to run major business operations that require a static IP address such as server management off a simple residential internet connection (they want them to take out the more expensive business account option). Thus, a new IP address is assigned whenever a new connection is established, which will happen on dropout/re-connection or modem-powercycle.

If the internet drops daily, this may be a sign of poor noise margins on the copper line (presuming ADSL) or other tolerance levels among personal equipment. If this is happening inconveniently frequently, contact your ISP so as to diagnose an issue/fault and/or request stability.