I just purchased this on steam, although I had this problem with the demo version I downloaded and played last night, also.
Essentially, after I go off the track during a race, all sounds except the narrator suddenly stop. No explosion sounds, no laser sounds, even the music cuts out. I DO hear the narrator, however ("LAST LAP!"). I can only get sound back if I exit the game and re-enter. Sound then works normally until I go off the track again (which is...*sigh*..inevitable).
I'm using an intel-i7 based motherboard with WinXP (32-bit), but I AM using an off the shelf sound-card, SounBlaster Audigy 2 ZS. Let me know what other informtion I can provide you to help track this down.
I think it's safe to assume that the lack of sound is what's causing me to lose every round, huh? ;-)
EDIT: I did some more experiements: Sound cuts off automatically after the first race, even if I DON'T hit a wall. Interestingly enough, I hit a few walls in that race without losing sound. When the race ended, the sound died until I rebooted (except the narrator).