MBA auto-ejecting USB-powered external HD

I have a new Apple-refurbished MacBook Air. When I plugged in a certain 2.5 inch USB-powered external hard drive, it would briefly mount on the desktop, and then disappear with the "Did not properly eject" error message. It will then reconnect and immediately disappear again. When I plug the hard drive into two other MacBook Pros (both running 10.9), it works fine. Also, a different USB-powered external hard drive worked fine with the MBA.

I am new to MBAs. Do they not work with some USB-powered drives? Could it be a Yosemite thing?

Computer Info:

13-inch, Mid 2013

OSX 10.10.2

500 GB Flash Storage

Processor 1.7 GHz Intel Core i7

Memory 8 GB 1600 MHz DDR3

External HD Info:

Western Digital (WD)

"My Passport"

WDBABM7500ABK-00

USB 2.0

http://support.wdc.com/product/install.asp?groupid=212&lang=en