Has email ever worked?
The only standard things that could effect email functionality like this would be either the SMTP Server itself (have you tried an alternate?), internet access or not having email addresses configured on the users extension.
Is there a more specific error in the log, the issue can sometimes be a mismatch between the IP address the request comes from and the registered FQDN.
"5.7.0 is a missmatch of your FQDN IP to the IP you are sending the eMail from.
Check under Settings Network that the IP there is correct and your FQDN resolves accordingly."