Type of burning programme do you use, and what is it's CD RW programe. In a lot of cases, it may be that these need updating, for instance a CD RW programme that Nero produced some years ago was called InCD, for a good while it was prone to exactly the same problems you describe, though it has been updated now and seems to be OK.
However, the best way to back up data is to burn a CD (or if your burner will handle it) a DVD R disk, these will be able to be read at will and provide an excellent backup system.
I am using Windows XP CD Writing Wizard to burn data to my CD-RW discs, with no problem; everything shows up fine. However, the next day, when I try to read what is on the disc the CD-RW drive cannot find any files. If I put this CD-RW disc into the other CD reader to try to read the files, this drive does not even recognize that a disc is present. Using several new discs from the same batch (Memorex) results in the same problem. However, burning CD-R discs (also Memorex) in this same drive leads to the retention of all my data; everything is fine. Problem is only with the CD-RW discs.
I am a novice in this area and would appreciate any help that anyone might be able pass on.