I wish to notice that if to copy files in the size up to ~1mb
that damages is not present.
There are no files, Mr. Anderson! That said, I had similar
problems when using cheap USB cables. Try getting a nice thick
expensive one. Hard drive itself may be the culprit, too. Try
attaching it directly and running several long tests with
smartmontools (from ports).
If you're looking for workarounds, try copying with rsync