On Server 2012 R2  I was unable to synchronize software updates in my ConfigMgr Current Branch environment. Server Manager kept reporting that the WSUS service was stopped. Each time I would restart the service, it would stop again.

When checking the ConfigMgr logs:

Wsyncmgr.log Sync failed: WSUS server not configured. Please refer to WCM.log for configuration error details.. Source: CWSyncMgr::DoSync
WCM.log Remote configuration failed on WSUS Server.

I previously had no issues with my SUP. Last change was that it was patched as it was a new environment. Upon more research I had applied patch KB3159706 

To fix this there were some post update tasks to do which I did not do:

Load up cmd prompt:

cd “C:\Program Files\Update Services\Tools\”
“wsusutil.exe postinstall /servicing”

Then open up Server Manager, add roles and features wizard, in the features section under .Net Framework 4.5, then under WCF Services, select to install HTTP Activation

After this I had to restart my ConfigMgr site server which had the WSUS installed and it was fixed (same issue after restarting the WSUS service, I needed to do a full reboot)