While getting "Outlook Anywhere" to work in our Microsoft Exchange 2007 environment I had to do a little trouble shooting. Here are some things to look for if things are not working.
Make sure you are using Basic Authentication with the RPC proxy.
Triple check that Outlook Anywhere is enabled on the Microsoft Exchange 2007 server and that the RPC Proxy is installed.
Close Outlook and open it backup with the switch /rpcdiag (Start, Run, Outlook.exe /RPCDIAG).
Also since you are using Basic Authentication you must be using SSL. The SSL certificate must be trusted by the computer that is running Outlook, so I suggest it is a third party certificate that came from a reputable online source. You can only use self-signed certificates if all the computers that will be connecting to Outlook Anywhere are also part of the domain that created them.
Maybe I should do a complete series of how to's in regards to Outlook Anywhere and RPC over HTTP.