I have a 2000 Challenger 14 and it does exactly the same.....just stops - sometimes when turning, sometimes when going straight. Is it likely that the key is just a little stretched and coming off the post?
Another year gone and this was becoming more regular. I thought is was the key so got hold of my spare (a lot more work to find it than I had expected) but that didn't help. Had a mate take out the DESS post and had the dealer quote on a new one - but that was a couple of hundred dollars. got hold of the specs and put a multimeter on it, was way off the expected readings he so pulled it apart and fixed what seemed to be a dry solder joint...
All fixed now - hasn't cut out since!