Almost losing my files on my USB external HD last week, thankfully it worked after long time looking for a solution on Google.
Here is my situation. I had my external hard drive disconnected from my Mac many times (with Mavericks OS), and finally my external hard drive was not showing on finder, including the partitions (I have two of them). So I tried to disconnect the HDD and reconnected it again, also waited for a period of time, and still could not see them.
However, I could see it on Disk Utility. You can hit “CMD + Space” keys, and will display spotlight, type, “Disk Utility” to open it. In case you need a new external HDD check out Amazon for the affordable best seller.