My passport keeps losing connection with my laptop

I have a WD Passport, WDBACY5000ABK-00.  I use it mainly to back up all my pictures.  When I connect it to my desktop, which runs Windows Vista, it runs just perfectly.  I can copy many pictures on there and I have no problems what so ever. 

But when I connect it to my laptop that runs Windows 7, after a couple of seconds Windows no longer recognizes my passport.  When I first plug it in, it recognizes it and I see all my files.  But if it stays plugged in for more than a minute or two, or I try to copy any files over to it, after about 30 seconds to a minute it stops copying and says it can’t find the drive.  Or it shows the drive, but it says the drive is empty, even when it’s not.  When I unplug it at this point, my laptop won’t recognize it again unless I reboot my computer and plug it back in.  I use the original cable that came with my drive, and I’ve had this problem from the moment I bought the drive a year or so ago.  I can also hear a faint ‘click’ like it’s turned off when this happens.  I’ve tried to update the firmware, but can’t because it times out.  I no longer have access to the desktop where it worked, so I really need to get this to work on my laptop.  Any suggestions on how to get it to work or why it seems to shut itself off all the time when I use it on my laptop?

Be sure to use the USB cable that came bundled with the Passport, longer USB cables or USB hubs can cause power consistences. There are also some laptop models that lower the voltage on some or all USB ports when they are not connected to power.