I suggest that you make some search in the forump on Copy Faled.
I have replied several times to this question.
ie.
www.jms2win.com/forum?func=view&id=681&catid=5#681
The reason is a permission problem.
Sometimes the owner or group of the files and folder are not compatible with the one that you are using to install the patches.
See also the user manual (trouble shooting) that describe this error.
One solution consists in using the Joomla FTP layer functionality.
Have a look in the tutorial step 15 that show how to setup the FTP Layer.
If you provide an FTP user and password to Joomla that has enough privilege, this should help you bypass the permission problem.