I now got this problem on my neck a couple of times, here is a fix

If you have a Windows 2003 server that after a while becomes unresponsive. The server will not accept new sessions either RDP, SMB etc. if you have an active RDP session that session will work, rather slow but it will work.

I have seen this problem on Windows 2003 servers with service pack 2 and the “problem” is network features (I also noticed that some versions of Symantec antivirus can get a similar problem). If your network equipment does not support these new features the server will refuse to work.

There are a couple of related KB articles that will explain this problem and fixes