I'm having issues getting application insights to report data to Visual Studio Online from behind our firewall. I opened the firewall rules noted in this article but it didn't make a difference. I've uninstalled and reinstalled several times. The only thing that is showing up in the Operations Logs is that it's periodically purging items in the "AppDiagnostics" queue since exceed the maximum allowed size of 15 MB (full error below).
Get-WebApplicationMonitoringStatus shows all the applications I would expect to be monitored being monitored.
The health service has removed some items from the send queue for management group "AppDiagnostics" since it exceeded the maximum allowed size of 15 megabytes.