So long as you still have the data in your system, it sounds like this is, actually, just a minor problem. You can always copy the info to another CD. I used to backup this way, and found that you could use a CD more than once, but eventually, you do have to throw them out and use a new one. Now, I back up to USB memory sticks, which I find easier, faster, and they hold more data. (And I back up all of my files twice -- to 2 separate memory sticks -- that way, if one doesn't work, for whatever reason, I've still got the other one as a back-up.)
But back to your problem -- you might want to put that same CD into another computer to see if the problem is with the CD itself or your system.