Because the auto-poweroff function is built into the enclosure, the simplest (and perhaps only) way of preventing it from kicking in is by creating a Cron Job that periodically touches a file on the drive.
Start by giving the drive (partition) a label name, if it doesn't already have one. This allows Ubuntu/Mint to automatically mount it to the `/media/
Then, in Terminal, edit your crontab by entering this command:
crontab -e
And add this line:
*/5 * * * * /bin/touch /media/
The Cron Job will touch a hidden file named `.stayawake` on the drive every 5 minutes, and redirect any resulting output (including errors) to `null` which is what you want considering the drive might not always be connected.
Note: The above Cron Job will only work while the user under which it was created is logged in.