|Sample from Event Viewer|
Lucky me I found the issue reading the following posts:
WSUS Post Deployment Configuration Fails on Windows Server 2012
It mentions: When using SQL for your database instance you must specify the name of your SQL server. One would assume if the database is local the wizard would find the instance without specifying the SQL server name. If you select Check Connection without specifying a server name it will return Successfully Connected to server. Despite this misleading result, it was not successful. The server name value it expects when running the Post Deployment step will be empty and will cause Post Deployment to fail.
WSUS install on Server 2012 Fails
It mentions: I solved this issue by opening IIS Manager and deleting the old WSUS web site, then running the Complete WSUS Installation again.
What you have to do is uninstall WSUS, remove the IIS website manually, keep the WSUS database (it won't be removed after all) and reboot the server. After reboot install WSUS again, choose to check connection with the SQL server filled in, and start Post Deployment. This time it will work fine again!