If you launch Windows Server 2012 R2 Essentials Backup Launchpad, and to your surprise it shows
Backup is not set up for this computer
it turns out, the fix is simple, takes about a minute. Not sure why this issue crops up occasionially in the first place, but at least there's no need to uninstall/reboot/reinstall the client connector. If the PC that has the error is powered up, and you're the admin, simply perform the following steps.
1) Launch your 'Windows Server Essentials Dashboard'
If this warning comes up, click OK
3) Click the 'DEVICES' tab, right-click the affected Computer, select 'Set up Backup for this computer'
4) For 'Choose a backup option' select 'Back up all of my files and folders (Recommended)'
5) When prompted to "Confirm items to back up" click "Save changes"
6) When prompted 'The backup was set up successfully' click 'Close'
7) To test whether backups are working properly again, you can optionally kick off a backup from the Dashboard, since you're there already anyway!
Right-click on the computer you just configured, select 'Start a backup for the computer'
8) If you'd prefer to run the backup from your client computer instead
Bring up the Run dialogue (Win 7 - Start, Run, Win 8/8.1, Win+R), and paste in the following