Rod's only too correct that -RW discs are more troublesome than -R discs. You're also correct in susoecting that some drives work better with some media brands than others, although it's a PITA figuring out which media brands work well with which drives. Recordable discs have been known to go bad halfway through a spindle, too, either from manufacturing variations or improper stoage of the discs (the NIST's
Care and Handling of CDs and DVDs has some useful tips there). By all means, try a different brand -RW media and see if that helps.
Another thing you might try: run a CD lens cleaner through the drive. -RW media is in general less reflective than -R media which is turn is less reflective than commerically pressed discs. It's possible there could be just enough grime on the drive's LED lens to affect reading the disc. It's more likely that a dirty lens would read with errors, not fail to register at all and be ejected, but it's something that's easy to try.