One problem related to engine stall has been reported for the 2012 Hyundai Veloster. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2012 Hyundai Veloster based on all problems reported for the 2012 Veloster.
While parked, car starts hard then will not shift, despite the dash saying it's in drive. Have to shut off, wait, then restart. At stop signs, car will stall then not restart. Once restarted, car will not shift. Need to shut off then restart repeatedly until it shifts. While in motion going straight on the highway, car will act as if it's lost engine power and then stall completely. Again, car will not start, and once it starts it will not shift. Again repeat the turn on/off process until it shifts. Has happened more and more frequently but dealer cannot give me an answer. This car is very unsafe to me and others on the road with it's unpredictability.