I'd try making your mail server have an alias IP address, in addition to its primary one. When the mail server shuts down, create the same mail alias IP address on the backup server.
The one problem is the ARP tables on your router may have to be cleared so that it can associate the new MAC address of your backup server's NIC with that of the IP alias.
You can do this by sending a ping to the router using the alias IP as your source address.
You should try it a couple times with a test system to be sure.
# ping -I alias-ip-address router-ip-address