The next step is to open Console (or Terminal, or access the logs via ServerAdmin if you prefer) and look at the logs. I've never seen a similar issue, so I can't even begin to guess what's happening. AFP logs would be a good place to start, but poke around whatever other logs that may be relevant and see if there are any clues. I have seen Servers have issues with all connections, but never more than a certain number, and 8 makes no sense.
Can you elaborate any more on what your network looks like and how exactly your server is setup, and how you set it up?