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So what you are describing is VERY VERY VERY difficult to troubleshoot or figure out.
First of all, we dont knwo WHICH device is causing the incomplete transfers....is it the Server? Is it the External drive? Is it the OS on the server?
Are you using any Virtualization for your servers?
Also....what is the OS you are using for the 2nd Server?
Also, are you using a SCRIPT to run the copy jobs? Or is this a Manual process?
Answer those questions....and i will try to formulate a troubleshooting process you can follow.
Usually it would be skipped because it was in use or otherwise locked and unavailable to the program doing the copying on the place it was being copied from.