Certain CD-R's not working in car..sometimes
Solution 1:
It could be a burner issue; try burning slower, at 4x or so, and see if those discs work better.
You can use the excellent ImgBurn if your normal burning software doesn't provide a friendly means of specifying the burn speed.
Oh, and make sure you aren't moving your laptop when you're burning.
Solution 2:
I used to have this problem, with a CD player in a Toyota Camry about a decade ago (and I honestly can't remember if it was stock or some brand).
I never did find out the deal (within a few years I had sold that car and installed a new one in my next car which natively played MP3's from CD-R's) but the bottom line is that your CD player was designed to play premanufactured CD's and you're asking it to do something it's not designed for, so it's natural to get mixed results.
But I did notice that some brands did better than others and that burning at a slower speed seemed to help. You mention your desktop burner seems to produce better results, see if you can make an image of the laptop discs and re-burn them on your desktop.
Basically it's always going to be a bit of a voodoo touch-and-go until you upgrade your arrangement. I'd recommend getting a player with either and 1/8" jack or an iPod cable and migrate your collection to an iPod and cut out the CD-R voodoo altogether.