external hard drive problems

with 2007 white macbook, using seagate go flex 1T external hard drive (not full, but huge, and holding thousands of large raw canon photographic images), the external hard drive is not appearing on my desktop when i plug it in...was told to see if it shows up in 'disk utility' and it is listed there, was told that is a good sign. downloaded the newest version of recoverx software, but have not used it yet, as when i opened disk utility and highlighted the seagate external drive, a box opened asking if i wanted to 'verify and repair' it, and i clicked yes. it immediately started to appear to be running the verify and repair...and has been for several days...the blue and white stripe at the bottom keeps flowing...given i am using an older white macbook and the external seagate drive is huge, how long can this process take, when should i decide it's not working, after a week, a week and a half, two weeks, a month, ten years? I do remember that when i used recoverx to recover a 16G camera card, it surprised me that it took 8 hrs...i don't know what the difference is between running a recovery software and verify and repair from the computer itself...