Start with analyzing Exim logs to learn what is the reason for delays. Perhaps you'll need to change logging settings in /etc/exim.conf to log all actions in order to find out more details.
You can do in shell with eximstats or using exigrep, or even less. Or just do it in directadmin on page «Mail Queue Administration». If you see on that page any delayed outgoing messages, click on them and learn details.
After that, you'll might probably want to fix it. Update us with your findings.