Hi Brian,
To determine which process is turning off the Google update services, you can try a clean boot.
A clean boot is the process of starting Windows without loading any third-party applications or services.
Reference: https://support.microsoft.com/en-us/kb/929135
Launch msconfig.exe.
On the Services tab of System Configuration, select Hide all Microsoft services, and then select Disable all.
Enable the check boxes for the Google update services.
Select Apply. Click OK, and restart Windows.
If the problem doesn't happen in the clean boot mode, follow the instructions under the paragraph "How to determine what is causing the problem after you do a clean boot" to narrow down the issue.