I found that power output of USB ports can vary a lot between systems so I don't like to rely on it for something like a HDD as you don't know from one system to the next if it will provide enough power.
I would use an external power adapter. If the enclosure does not have a separate power port you may need to get creative and inject 5v into the USB one. I've done this, it's safe, just don't get the polarity mixed up.
Though it could also be the drive is going to sleep as suggested. If you can't find a setting to turn this off a quick and dirty way is to write a small script that loops and just writes small amounts of data to it. I had to do this on a Linux server as I mistakenly used drives that go to sleep to build a raid array and the drives kept dropping out of the raid. So I made a script that just does a "dir" and writes the results to a text file then deletes it, and the script runs once a minute. It was enough I/O to stop the drive from going to sleep.