[exim] (110): Connection timed out

I have a user who contacted me, saying that he is not getting his mail.
This is on a server that processes mail for thousands of domains and lots
of messages every day.

So I checked the logs and see EXIM reporting a connection timed out. That
normally indicates the remote server is offline, firewall, networking issue
etc.

2014-11-12 15:59:22 1XoJ6d-0006S3-Io exchange.lahore.com [82.71.51.200]
Connection timed out
2014-11-12 15:59:22 1XoJ6d-0006S3-Io == shahid@??? R=ik_router
T=remote_smtp defer (110): Connection timed out

A manual connection to the server via telnet works, I can connect and
deliver mail.

Seems odd.

In rare situations where there is a routing issue or firewall issue I can
clear the queue for a specific domain by routing mail pending for the
domain to another of our servers at a different datacenter. Essentially
route around the problem. So I tried that, I use this little router:

# move mail to another server if it is stuck on this server for some reason
clear_queue:
driver = manualroute
condition = ${if match{$domain}{lahore.com} }
route_list = * "122.103.250.10"
transport = remote_smtp
no_more

That normally will just direct any mail to another server and it is
processed and delivered from there.

This one specific domain, when I try the clear_queue router - it will
report connection timed out. I know there is no firewall rules as I control
both networks, no ISP block and these servers communicate all day long.

How do I go about debugging what is actually going on here?