Windows update failing with error 80244007 "could not search for new updates"

Since you're connected to a domain, I assume it's an invalid Target Group name. So what you have to do is to open the registry, and then go to : HKLM\Software\Policies\Microsoft\Windows\WindowsUpdate

And then look for Target Group key, export it first (just a backup) then delete it.

Now, restart your computer and check Windows Updates.

I got the same error on a Windows 10 (1511) computer. In my case, deleting C:\Windows\SoftwareDistribution\DataStore\DataStore.edb worked:

net stop wuauserv
del C:\Windows\SoftwareDistribution\DataStore\Datastore.edb
net start wuauserv
wuauclt /detectnow

This solution was not my idea, but was suggested by Frank Maxwitat here.

The problem appeared after running the Server Cleanup Wizard on the WSUS server used by this computer. However, there was a different problem before running the cleanup, so it might be that this problem simply got hidden by the other problem before the cleanup.