External hard disk often not mounted

Try resetting the SMC and PRAM

OS X: What is Safe Boot, Safe Mode?

Intel-based Macs: Resetting the System Management Controller (SMC)

About NVRAM and PRAM

If you tried the resets the other poster suggested it might be several problems. I used a produce named Scannerz to find some problems with my system, and I was quite impressed with it, but I'm not sure that's what you need. They do, however have a how to section and a write up on various types of hard drive problems. To get to it, their main site is:

http://scsc-online.com

and go to the how to section from the top link and then look at their write up on hard drive problems.

From memory, the following might be the problem:

1. An OS bug in Yosemite - to test that, if possible, you might want to put an older version of OS X on another external drive, maybe an old one you don't need any more, and see if the problems with the WD still exist. If they go away, it might be Yosemite.
2. Bugs in the driver - if you've installed manufacturers drivers there may be an incompatibility problem. WD has had problems with them before, as have other manufacturers. Most people recommend not installing third party drivers because when OS changes occur, sometimes a driver that was working with one version of the OS stops working properly with another. See if the manufacturer has updates available for the driver.
3. Bad cable - If the cable is erratic at start up the drive may or may not see it. Scannerz can test that sort of thing but you could also try another cable. I think this is less likely than the other two because I would think the drive would periodically eject in the middle of use and not stay connected, but it's worth a try.
4. Power supply problem - this I assume is even less likely than the rest unless this drive is port powered, and I don't think it is.
5. Drive timeout - Some WD's had some type of problem with drive timeouts and it's a firmware problem. It occurred on drives made several years ago. Some guy on another forum, I think it was MacRumors.com reported this.
6. A logic board problem with the integrated I/O controller - this is probably the least likely of all. Scannerz can test that but if it finds problems you won't like what it's telling (logic board has problems). I think this is the least likely of all.

Personally I would suspect items 1. and 2. above as the most likely. I would also recommend going to WD's website and seeing if there are other mentions of the problem and possible solutions.

Good luck.

I wouldn't assume it's the logic board. Possible? Yes. Likely? No. Why? Because there are tons of reports on various web sites about USB drives behaving erratically on some systems and not others.

As ridiculous as this may sound, plug the external drive into a USB hub, then plug the hub into the Mini and see if the problem persists.

If it was a logic board fault it would behave in one of two ways: a manner similar to a unit with a bad cable making intermittent connections, meaning the unit would come online and go offline sporadically, or the unit and all other units would simply not be seen at all, as in total failure.

Make an appointment at the Genius Bar of an Apple store.

Apple Retail Store - Genius Bar