Thank you for your post.
When FileMaker Pro/Go connects to a hosted file, the hosted file continually checks to make sure the client is still connected. When the client closes the file, the host will detect the client closing and no longer monitor the client. If the client loses connection (either by computer freeze or computer going to sleep), the host will try for about two minutes. If the client cannot be detected, then the connection is dropped.
In your case, the host file can no longer detect your accessibility, so the connection is dropped. Monitor your network to make sure port 5003 remains open. If there is a firewall, temporarily turn it off. Try resetting any routers.
Does the disconnect only occur with your computer? That is, do others also run into the same issue?