Historically, the problem has been that many USB-powered drives can't get enough power from a USB port after they begin to age. The Passport is bus-powered, getting all its power from a USB port. Not the best solution for a desktop computer.
To get such a drive going again, you need one of two workabouts:
1) a powered USB hub (has its own power supply to make up the shortfall) that goes between the external drive and the computer.
2) use a "Y" USB cable to get power from two USB ports simultaneously (such as http://eshop.macsales.com/item/OWC/USB2AYMBPB/)
Also, WD uses an odd proprietary formatting scheme that is of itself a problem area. WD makes very good bare drives but the enclosures into which they put them to make an external drive are not very good and not particually Mac-Friendly. The formatting makes them harder to use.
Once you get the files you need off the external, consider erasing and reformating it to Mac Extended Journaled using Disk Utility. That often makes the drive more reliable without having to revert to USB hubs or special cables. It gets rid of the proprietary formatting that seem to contribute to the problems.
I have three external drives. All have WD bare drives inside but none are in WD encosures. By far the best enclosures for Mac external drives are those from OWC:
http://eshop.macsales.com/shop/firewire/1394/USB/EliteAL/eSATA_FW800_FW400_USB
I have two of the desktop model shown and one of its portable version for my MacBook Pro. All three have given me superb service and zero problems.