Sorry no, but there was a way we troubleshoot
So I'll share. We would tether the android to our PC and from there we could use the use tools of NSLOOKUP, TRACEROUTE and well, you as the IT lead would know the rest.
Armed with that we would show this to our cellular contact (we were working on a system that involved many thousand mobile clients) and they would look into the issue.
But in your case I think you need to know that such is best solved by more than one email access path.
I can hope you tried at the very least different IP Ports on your server.