Problem copying image files to My Passport from compact flash card in camera or reader, using a Mac

I recently purchased a My Passport portable drive for a friend who is a photographer.  He has a new MacBook Pro and a Nikon camera that takes large size files.  Using a 32 gb compact flash card either through the camera or a card reader, he has attempted to copy his image files from the CF card directly to My Passport, with both being connected to and recognized by the Mac computer.  In every attempt, My Passport will only copy half the files and then stop.  On a second attempt, it takes half of the remaining files and then stops.  On a third attempt, it again takes half of the files that remain, although all the files have been selected for copying.  If there are 400 files, My Passport takes 200 and stops; the next time it takes 100 and stops, and so on.  There is no problem whatsoever in copying the files directly from the computer to My Passport.  All the files get copied immediately.  But my friend would like to copy from the compact flash card to My Passport while both are connected to the computer.  The My Passport he is using is for both Windows PC’s and Macs.  Any good advice will be greatly appreciated.

If the drive is being use for both systems windows and Mac, the drive should be formatted in FAT32 and remember that a Fat 32 formatted drive will have issues with big files.  By any chance do you have files bigger than 4 or 3.5GB

The drive was formatted for ExFAT.  Would that be the problem?  We would like to use if for both PC and Mac but if that is causing a problem, we can limit it to Mac.  The individual  files range from 70 - 77 mb each.  No file is 3.5 GB.   Thank you for your assistance.