Alan,
I'm not sure what other application/sites your referring too, but if they aren't making outgoing connections and doing similar behavior to JFBConnect, it may not be a similar situation.
When connecting to Google+, JFBConnect needs to connect to the following URLs:
https://www.googleapis.com
https://plus.google.com
https://accounts.google.com
The best thing to test is to check the responses to the following commands for each of those URLs from the command line on your server:
nslookup www.googleapis.com
ping www.googleapis.com
Try for each domain. Feel free to post the results, but they generally should be:
* nslookup - a very quick response returning an IP Address that should be used to connect
* ping - a repeated sequence of how long it takes to make a request. Generally, each response should be under 50ms and there should be 0% packet loss
It definitely sounds like a server connectivity issue since there's *nothing* in JFBConnect that should possibly take that long to process. The only thing that could be causing that is waiting for a response from Google.
You may need to get your hosting company to help with the tests above, or ask if they need to whitelist outgoing connections to specific domains (which is sometimes required). Hopefully, that will help narrow things down though.
Please let me know what you find,
Alex