I seem to have solved this issue for me by using Terminal instead of Finder to copy. Here's the sequence of steps:
1. Open terminal.
2. Go to desktop by typing:
$ cd /Users/yourusername/Desktop
3. Create a destination folder by typing:
$ mkdir DestinationFolder
4. Go to the folder containing files you want to copy, in my case:
$ cd /Volumes/EOS_DIGITAL/DCIM/100EOS5D
5. Use this command to copy all files from 100EOS5D to DestinationFolder
$ cp -av * /Users/yourusername/Desktop/DestinationFolder
where -av instructs the copy all files (this what * means) from current directory to DestinationFolder, and options "-av" mean "archiving" and "verbose", that is copying all files as is and displaying progress in terminal window.
I've been having this problem since, if my memory's correct, upgrading to Snow Leopard. This solution worked on new MacBook Pro 13'' Retina (late 2013) with Mavericks 10.9.1.