When we tested the email notification via the "Test" button, emails were sent. Automated mail notifications could never be sent and resulted in this error. In our case, the problem was caused by insufficient file system access rights to the %TEMP% folder. After granting the NetworkService user read/write access to the %TEMP% folder this problem was solved.
In my case, whenever I clicked on the "Test" button, the sample e-mail worked, but the automatic e-mail never worked. We use McAfee Antivirus software in conjunction with ePO agents in our company. It turns out that the default policy sent to all PCs and servers is to block SMTP traffic (to prevent spam relays). Once I had an exception policy applied via ePO Orchestrator for this particular server which would allow SMTP traffic, then the problem was fixed.
As per Microsoft: "If the network's e-mail server is offline, WSUS 3.0 will silently fail to send e-mail notifications. However, it will write event 10052 (HealthCoreEmailNotificationRed) in the event log". See the links to "Release Notes for Microsoft Windows Server Update Services 3.0" and "Microsoft event 10052 from source Windows Server Update Services" for additional information on this event.