External disks UNMOUNT when I try to verify with Disk Utility?

I have two Lacie external hard drives, one of which is for general backup use, the other is for time machine.

For some reason today, the Time Machine backup disk suddenly disappeared from the desktop. I rebooted - and it was back. It ran a backup, no problems.

To be safe, I decided to run disk utility to try and verify both of my external drives. On running disk utility / verify disk - the verify disk starts up, but then suddenly the disk unmounts and the verify stalls out. When I tell it to stop verify - the disk remounts and pops right back up.

Any idea as to what is going on?

 

Now I feel a little silly.

I am no expert with disk utility, but I believe it "unmounts" the disk as it goes about its work - because I now see that as I let the process continue it has continued and appears to be nearing completion of the verification process!