As noted in reply to the original topic creator, an iPod connected to the car audio system is NOT playing the songs. The car audio system is doing the song playing, and the iPod is just a USB storage device with song files (accessed by the car audio system). It's like connecting a common USB flash drive (with song files) to that USB port. Therefore, you cannot directly compare playing the iPod as a music player to using it as a storage device connected to the car audio system; the iPod is being used in different ways. It could have data corruption (or a hardware problem) that affects one usage but not the other. Or if this never worked properly before, your iPod model may not be compatible (check user guide for car audio system for list of compatible devices).
Also as described in the previous reply, you should try doing a Restore on the iPod using iTunes. Did you do that? If the problem is only data corruption (not a hardware problem or incompatibility), the Restore (and re-sync) should resolve that problem.
You may want to consider using an inexpensive USB flash drive (with song files loaded) instead of your iPod. Here's one that barely sticks out of the USB Port (no cable needed) that has same storage capacity as your iPod nano
http://www.amazon.com/SanDisk-Cruzer-Low-Profile-Drive-SDCZ33-016G-B35/dp/B005FY NSZA (or get higher capacity)
(EDIT: Something is messed up with adding links to posts. Search on "SanDisk Cruzer Fit" for the above item.)
You can load it up and leave it connected to your car audio system, except when you want to update its song files. You'll avoid the wear-and-tear of constantly connecting and disconnecting your iPod, and the potential for heat/cold damage (or theft) if you forget and leave your iPod in your parked car. Use your iPod as a music player, not a song storage device for your car.