I can confirm this to be an isolated bug in Windows 7. I am having the exact same problem on one of my systems as well. Perhaps it may be related to OneDrive in some mysterious way. In any case my work around is:
After you open My Documents from the Start Menu -> It opens the Document Library -> Then under the document library there is the parent folder in question. The physical location of this folder is C:\users\owner\documents\problematicfolder
If you rename the problem folder to a different name, you are able to restore the New Folder Context Menu or File Menu->New-> Folder.
Otherwise, once the My Documents window is open if you look to the left window pane where it shows the selected Library if instead you select the Document folder instead of having the Library selected the problem will subside.
It appears only to fail to allow you to create a new folder when: Libraries is selected in the left window pane and under a specific folder name that prevents you from creating a new sub folder within the parent problematic folder.
However, if that parent problematic folder is renamed to something else, it will allow you create a new sub folder in that renamed folder. It must be a bad index in the libraries enumeration and I have no idea how to reset that reference.
Disabling and Enabling the libraries after a system reboot doesn't help. Disabling libraries all together and rebooting fixes the problem. However, then the Documents shortcut will no longer appear in the start menu and manual shortcuts will need to be placed on the desktop for direct access to the document folder.
I wish Microsoft would never have introduced such a complicated and unnecessary library solution. Windows was great before Libraries I don't know of anyone who uses the feature as it was intended.