Is the enclosure's firmware up to date?
And your USB3.0 / SATA drivers (as applicable)?
The Mediasonic area for the drive has links to various drivers as well as discussion about problems/solutions with a few different firmware versions: forum.mediasonic.ca/viewforum.php?f=27
The USB / SATA drivers are what I would try first.
Since the process is actually crashing, from the screenshot in your last reply, it's worth checking to see if a crash dump has been created matching the date and time of the crash. If there is one with the right date & time, please zip it up and send it to us and we'll see if it reveals anything. (It may not, if something low-level like a driver or antivirus is crashing, but it's worth a look.)
If you haven't already, please try changing the Preferences / Miscellaneous / Advanced: copy_buffer_size setting to e.g. 1024 KB and the copy_nonbufferio_threshold to 0 (i.e. zero) to see if it helps avoid the problem. (If it doesn't, please reset them both back to their original values. There's a Reset button at the button of the Preferences page which resets the currently selected item.)
Another thing to try, since it's a crash and not just the drive disconnecting itself, is copying exactly the same files on to a local drive, in case it is something to do with the files and not the drives. (That could be cause by antivirus, for example.)