I haven't found much information on that specific error. You can think of 0x80080005 as an "access denied" message. Usually this is a permissions issue and can appear on almost any action depending on what's being accessed. This specific error context appears to relate to the system protection function. If system protection isn't working, you won't be able to create automatic restore points when you apply updates.
If you haven't already, turn on system protection for the C drive. Then, see if you can manually create a restore point.