My external network interface on a gentoo box will produce these errors intermittently (maybe 3-4 a week). It is hooked up to Optimum online, and gets its IP via DHCP. It's always-on, and it almost never loses connection (when it does usually I or one of my roommates notices it).
eth1: failed to renew, attempting to rebind
I'm trying to understand what might produce these errors.
When a DHCP lease expires, the DHCP client attempts a renewal - it contacts the original leasing DHCP server, requests a new lease, and if everything goes well it gets one and goes merrily on it's way.
After a period of time, if it doesn't get a response, or it keeps getting negative responses from the original server, it attempts to rebind.
This is essentially the same process as it uses on power-up when it's first requesting a DHCP lease - it sends out a broadcast asking for DHCP servers, and binds to the server that responds positively.
If you keep getting these messages it can indicate a DHCP server misconfiguration, an overloaded DHCP server, or a short timeout period in your DHCP client for the renewing process.
You can get more detailed information at the TCP/IP guide.
-Adam
I would like to add one correction to answer from Adam Davis. The DHCP renewal will happen not after the lease expiry, but with in the lease active time. There are two timers, T1 and T2. T1 being smaller time than T2. T1 is the time at which client can start RENEW process. ie, client can send RENEW at that time and extend the lease. if the client is not successful in renewing the lease with the server, it will broadcast the DHCP request (setting the IP to broadcast, so request will be send to all DHCP Servers in network) for rebinding. if any server can successfully cater this request, the lease will be extended with the server. So if you are not getting this error always, no need to worry, the RENEW process might not have completed due to some reason at that particular time.