External Hard Drive

I have a Mac book pro 10.7.5... I bought a Western Digital My Passport for Mac to put all my music on. I plugged it in an it worked great for the first day but then after that it kept not recognizing it an disconnecting its self / an disconnecting in middle of downloads. Now when i plug it in i dont even have a icon that comes up for My passport for mac.The light blinks an everything so i know it works. I plugged it in the another laptop (not a macbook) an it comes right up but i cant do anything with it clearly cause its not a mac. i just wanted to see if it worked. Any ideas what i can do to make my mac read my Western Digital. ?

Is it getting enough power? does it have a USB cable with two connections in one end?

Are you "unmounting" the drives before you unplug them?

I agree with mrplow in that I have only once had this problem (not Western Digital, actually Seagate) which turned out to be a power issue. It appeared to function okay to start with and then intermittently failed to mount properly.
I presume you are connecting the EHD directly to your Mac and not through a hub? In my case, the Seagate did not have a double USB connection and Seagate refunded the cost. As your purchase is apparently recent, WD should do the same....

Ian