Hello Jacob. I'm going to start by letting you know that you may get a quicker response if you reach out to Support to have them help you track this down, but here are some things you might check:
It is possible that this is due to your 2008 R2 servers if you're running WSUS 3.0 (if that were the case your Windows 10 machines likely wouldn't be getting MS updates either):
Policy and Certificate are definitely steps you want to start with.
You can check the Windows Update logs on a machine to get additional information:
If you do find an error code, you can reference this KB to see what it might relate to:
Thanks for the response.
The Win10 machines are getting their Windows updates just like they are supposed to.
Some GP settings I had to manually change due to our policies not correctly applying to Win10 machines, but I knew that was a strong possibility when I started testing. For my purposes, I manually changed all of the settings I needed on the machines in question. Other policies, such as certificates from the server, applied correctly and are present on target machines.
Running through the Windows Update logs, the errors I have seen simply say that the download failed. The error codes suggest a Windows Update database file corruption as the reason, but I had already run the troubleshooter and manually cleaned out the Windows Update files and the error code shows up both before and after. When I checked the Patch Manager, it gave an "Not Installed" status, rather than a "Failed" status.
I will probably have to get with Support on this. Thanks for your time though!