How can I have SQL Server listening on more than one IP address? I have a an SQL server that normally listens on a private IP address (10.x.x.x). However, I would like to be able to connect to the database over the public (31.x.x.x). I tried to enable this tonight, but when I restarted the SQL Server service, the server wasn't listening on the internal IP address any more.

I was using the configuration manager to let the SQL Server know the IP addresses it should be listening on.

I am running SQL Server 2008R Standard.
On the Protocol tab of configuration manager, there is a "Listen All" option, make sure that is set to yes. 

Keep in mind that having an active listener on a public connection is asking for trouble, best to do it over a VPN, or filter allowed incoming connections by IP address, or at least use something other than the default port.