You don't mention what OS or SS version you're using, so this will be a bit of a generic reply.
First step would likely be to ensure that your server can accept remote requests from inside the network. I would get on your laptop or some other end-user box on your home LAN or wifi network, ensure you're able to "see" (ping) your server, and then try to hit up Subsonic using the server's local IP address, such as:
http://192.168.1.1/subsonic/..... etc.
If that doesn't work, then there may be some firewall or internet security apps on your server blocking the incoming requests. Whatever port you're running SS on on the server, make sure it's open and that other machines on the inside can bring up SS successfully.
Once that's in place, then you can move on to the specifics of why an external box out on the internet can't reach it (did you change or reset your router settings, perhaps?)
Supra92