I just swapped out my old external drive for a Western Digital Elements 2 TB drive and I discovered something I hadn’t seen in the instructions.
I formatted the drive as Mac OS Extended, GUID Partition Table. Apple TV didn’t recognize the drive and rebooted every time I tried to switch to external. When I reformatted as Mac OS Extended, Apple Partition Map, everything worked fine.
So if you’re reformatting the drive, be aware of which partition scheme you use.