The error message appears as below.
There was an unexpected error in the property page. System Restore encountered an error. Please try to run System Restore again. (0x81000203). Please close the property page and try again.
After exporting the registry before and after and then comparing, I found the UpperFilters were deleted for the Storage volumes class. As far as I understand it, you need both Upper and Lower Filters in any given case.
To apply the fix, copy the following blue text, paste it into Notepad, save it as "repair.reg", then double-click to Merge it with the registry.
Windows Registry Editor Version 5.00
After applying this, restart the machine and try to open System Restore again - the error will disappear.
Tools used to help investigate
This error is also caused by other programs like TuneUp Utilities - see this Microsoft support page.