[exim] TLS error on connection

I've just put live a brand new shiney Centos 7 server to replace my aging
Fedora system. One of the reasons for doing the upgrade was to try to get
rid of the errors that prevented some sites from sending emails to us.

Unfortunately, I'm still experiencing the same errors on my new server.

I'm getting log entries like:


2015-08-27 14:00:04 H=mx-relay33-dus.antispameurope.com [94.100.134.233]
Warning: notquit: 94.100.134.233 failed with command-timeout

2015-08-27 14:00:09 TLS error on connection from
mx-relay33-dus.antispameurope.com [94.100.134.233] (SSL_accept): timed out

2015-08-27 14:02:03 SMTP command timeout on connection from
mx-relay42-dus.antispameurope.com [94.100.134.242]

2015-08-27 14:02:03 H=mx-relay42-dus.antispameurope.com [94.100.134.242]
Warning: notquit: 94.100.134.242 failed with command-timeout

2015-08-27 14:05:03 SMTP command timeout on connection from
mx-relay35-dus.antispameurope.com [94.100.134.235]

2015-08-27 14:05:03 H=mx-relay35-dus.antispameurope.com [94.100.134.235]
Warning: notquit: 94.100.134.235 failed with command-timeout

2015-08-27 14:05:13 SMTP command timeout on connection from
mx-relay31-dus.antispameurope.com [94.100.134.231]

2015-08-27 14:05:13 H=mx-relay31-dus.antispameurope.com [94.100.134.231]
Warning: notquit: 94.100.134.231 failed with command-timeout

2015-08-27 14:06:03 TLS error on connection from
mx-relay42-dus.antispameurope.com [94.100.134.242] (SSL_accept): timed out

Can anyone suggest what could be causing this, or at least where I can start
looking to investigate the problem?

As the new server is significantly bigger / faster than the old one, I don't
think performance is the cause. I have noticed that when
I 'tail -f /var/log/exim/mainlog' it scrolls up my screen much quicker than
the old server did so I think that performance may have been part of the
reason originally