You are correct.... that is not supposed to happen.
First off, if a flash drive (or any drive for that matter) gets full, the computer will give you an error message telling you so... it's not just going to pretend like everything is fine and then surprise you with missing files.
Second, a 2GB flash drive should be able to hold at LEAST 500 songs.
To fix this problem, try formatting the flash drive (go to "my computer", right-click the icon for the flash drive, and select "format"). If that doesn't work then you may have a defective drive.... take it back to the store and make them give you a new one.