IMHO, most probably that is a compatibility issue. Slightly different CD-RW media, slightly differently wearied CD-Drives, a bit of dust on CD-recorder and/or CD-player lens, etc.
Nowadays we all are too used to things that 'just work', and nevertheless there were times when one had to unplug network cable and do not touch nor keyboard nor mouse so that not to interrupt CD writing session...
Can you write other things on your CD-RW's? Data files, mp3's, movies? When is the last time you cleaned your lens? I agree with ugnvs, are you doing to many other things while burning? Even with multi-core processors it could cause problems. Can you burn .cda on a CD-R with no problems? Can you write DVD's? What software are you using to format/wipe your re-writable disks? Just some thoughts on trouble shooting for you.
Could be, I would try cleaning the lens on the car's CD player first, and then see how it plays a commercially made CD. If that works then try your CD-RW.
I installed a radio with a USB port in my older vehicle years ago, and most newer vehicles now have that. It was great to get rid of all my CD's and CD cases.
I run a 64 gigabyte USB drive, so have thousands of MP3's on it. Something to think about for the future.