I have a 2003 tiburon and when you are going down

I had this problem with my 2003 Tiburon SE. Dealer couldn't diagnose the problem - they said everything was working fine. By trial and error I discovered that when I disconnected my aftermarket CD player, the car was fine. Re-connect the CD player and the problem would occur intermittently.

I think the problem was that the CD player was drawing too much current from the car's electrical system, thus through the Body Control Module, or BCM. The BCM would overheat and shutdown, turning the engine off with it. Shutting off the ignition and re-starting the car would reset the BCM and all would be fine for a while.

Disconnect any aftermarket electronics you may be using (stereo, cell phone charger, etc...) and see if that helps.

Good luck.

Have it diagnosed. Too many possible causes of the problem you describe. Take/Tow your vehicle to an authorized Hyundai dealership and pay the diagnostic fee... they will tell you exactly what the problem is and the cost of parts/labor to fix it... at least this way you'll know what the problem is and what's required to fix it.