To make my long text short:
It seems the described problem occurs, because Endnote exploits the capacity of the NTFS file system in path length (may be also FAT32) to a degree, that is not reliably supported neither by the microsoft native programs like ‘copy’ nor by many other programs like ‘Adobe Acrobat’ or ‘Acronis’ backup software.
So handling the created attachment archive savely is only possible with Endnote itself.
That is not a typical behaviour of files. So it might be changed or the consequences should by announced more prominently to make the users aware of this pitfall.