I've just had a similar story.
I have a 5-year old WD My Book, and it started misbehaving after I got a new MacBook Pro w/Retina Display about a month ago. I usually connect it to the MBP about once a week, and today it got into the "Looking for backup disk" and hung there. The disk was accessible and I could examine it in Terminal, but Time Machine couldn't.
First, I tried to power-cycle the WD ... that didn't help.
I removed the com.apple.TimeMachine.plist ... didn't help.
Then, I power-cycled the WD again, and also restarted the MBP, and let them sit for a few minutes... And this time it worked!
As I mentioned above, this is not the first problem I had with this WD drive. Right after I bought the new MBP, and after I used TM to transfer all my files to it (which worked great), it died on me and I had to reformat it, losing a lot of old backups in the process. Since it's 5 years old, it may be time to replace it; but in fact, it seems like it's working fine for non-TimeMachine access.
Does anyone have suggestions on good, reliable external hard drives? I only need 300-500GB.