A lot of companies have measures in place to prevent outgoing ICMP requests, TCP connections to ports other than 80/443 for example, or even to prevent you from reaching the internet directly by (transparently) proxying your traffic.
Under an internet connection I would understand any way to contact the outside, be it UDP, TCP or ICMP. Depending on what your application needs to contact the internet for, I would suggest to check over the same protocol, as that is the only thing that matters to your app.
If your application uses HTTP to communicate to an external source, try to connect to a few sites you would suspect to not be blacklisted and that have a reliable uptime. Like google.com, microsoft.com, apple.com, and so on...
Edit:
I am unsure what the specifics are, so let me give you an example with a hypothetical situation.
Application A collects data on the system it is running on and forwards it to a Web Service listening on yourserverhost.yourcompany.com:80
Application B would basically take over the job of the Web Service when it is down and log everything so no data is lost.
- When all is well, App A will be sending the data to your web service
- Once this connection drops, you immediatly launch App B (the obvious remark here would be, why not keep App B running as a failsafe)
- App A connects to App B and forwards what it had been buffering
- App A continues to try to reestablish the connection to your Web Service and once it is back up will request App B to stop
If the problem you are facing is nothing like this, please provide a more concrete description of what App A and App B are supposed to be doing. I will be more than happy to help.