WD Drive Cannot be Repaired but program still running

I have an external hard drive that I use to run my iTunes, iPhoto library and store various other documents. Recently, it stopped connecting to my MacBook Pro.

I can only see my WD Ultra external hard drive in Disk Utility (it won't show in Finder). I tried to repair it in Disk Utility, but it told me it couldn't be repaired and gave me this message: "You can still open or copy files on the disk, but you can’t save changes to files on the disk. Back up the disk and reformat it as soon as you can"

However, disk utility still says "verifying and repairing partition map" and "checking prerequisites." What do I do? Do I cancel it? Is it actually repairing or is this a glitch?

And how can I copy my files when I can't see the drive anywhere other than Disk Utility? Please help!