I asked something similar recently because when I was waiting for emails to download, unless progress bar is moving you don't know if anything is coming in as you do on Windows with the flashing internet monitor icon in the bottom corner. Sometimes there is a fair delay in emails even though you know they should be there because I've already downloaded on the iphone, but there is nothing to show that one. And that is a time like you I am not sure if it's connected, I'm sure there is an app for that somewhere and someone on here, will probably be aware of it. There is an internet connection monitor but don't know that will do your job. It's not common because for most tasks something will come up to say you're not connected. If you are on WiFi the logo up top 'should' start moving when connection is lost or intermittently cuts out.