Very strange.
I also copy my images with a card reader and never installed the camera software (Canon 30D). So I don't think I can specifically help you with this exact problem with the software. But maybe observing the following may help:
1) When you shoot RAW+JPEG and you copy all the JPEGs over to the computer, is the memory card completely empty in the camera or does it appear to have "some photos" left on it? This may be all those RAW files if the software just isn't copying them over (though doubtful since some got copied over very recently but not all the old ones).
2) Double-check the software to see if it may be copying the RAW files to a different location than the JPEGs. I'm not sure why it'd be doing this, but it's probably worth a look just to be sure. (Or just do a search on your computer for .CR2 files if you don't have many on there in the first place)
3) If you do have a card reader, shoot RAW+JPEG and ensure that you're seeing both on the card before you try using the software - just to make sure that both file types are being captured and saved in RAW+JPEG mode. I would hate to think that it's not, but it's probably worth a minute to check.
My mind is officially boggled by all this.
One more reason to just use a memory card reader 