My process is to drag files or folders from one location to another. Sometimes it works, but it takes a VERY long time. Sometimes it does not work. For example, I tried to move a folder with 329 images. LR processed for 13 hours and moved 58 images; then it stopped and gave the message "…error copying files to the destination you selected. The following files could not be copied." Then it noted the files not copied. Does this look like a LR problem? A hardware problem? Any suggestions on how to fix would be appreciated.
Sometimes, if you have a lot of images you are trying to move, it can be easier to do it using your operating system. Arrange all of the images into folders underneath one master folder, and then move that folder to the external hard drive using Finder. Then when you start Lightroom it will indicate that the folder is missing. Right click on the topmost folder and update the folder location.
Jim has a very good suggestion. There are many factors at work here:
1) How are you connecting the external drive to the computer?
2) How big are files (329 x 1MB is not the same as 329 x 25MB)?
3) What is your computer specification?
4) Do you have any power saving settings on (in particular something that would send the computer/hard drives to sleep)?