I actually have a similar setup with one of my machines. I have the viewer, host, and server all on this one machine. Works fine for me. Make sure that in your "host" settings for this machine, that you use an IP address of the machine itself under internet ID settings, custom server address. However, I have also opened the port in the router for this machine, so I am able to do a direct connection straight to the host whenever I'm at another location remoting into this machine.
If you can connect and only occasionally have disconnects, that might point at possible network connectivity issues. Brief network disruptions (for whatever reason) may go unnoticed when you use a web browser, but become immediately visible when you need to maintain a long lasting connection.
That said, from your description I can guess that your Host connects to the server on the same machine. In the Host's internet ID settings try specifying the server name as "localhost" or "127.0.0.1" instead of the server's external IP/DNS, to eliminate a possible loopback issue.
In either case it would help to look at the Host log.
Thanks for your reply, and thanks to the other respondent as well. I didn't realize it yesterday but it turns out that I am in fact having intermittent packet loss /connectivity issues and will have the ISP work on correcting it.
I will also have my developer change the hosts settings as you describe.